diff --git a/src/gt4py/next/iterator/transforms/global_tmps.py b/src/gt4py/next/iterator/transforms/global_tmps.py
index c423a3c277..4f4fd053b2 100644
--- a/src/gt4py/next/iterator/transforms/global_tmps.py
+++ b/src/gt4py/next/iterator/transforms/global_tmps.py
@@ -15,7 +15,7 @@
 import dataclasses
 import functools
 from collections.abc import Mapping
-from typing import Any, Final, Iterable, Literal, Optional, Sequence
+from typing import Any, Callable, Final, Iterable, Literal, Optional, Sequence
 
 import gt4py.eve as eve
 import gt4py.next as gtx
@@ -150,20 +150,54 @@ def canonicalize_applied_lift(closure_params: list[str], node: ir.FunCall) -> ir
     return node
 
 
-def temporary_extraction_predicate(expr: ir.Node, num_occurences: int) -> bool:
-    """Determine if `expr` is an applied lift that should be extracted as a temporary."""
-    if not is_applied_lift(expr):
-        return False
-    # do not extract when the result is a list as we can not create temporaries for
-    # these stencils
-    if isinstance(expr.annex.type.dtype, type_inference.List):
-        return False
-    stencil = expr.fun.args[0]  # type: ignore[attr-defined] # ensured by `is_applied_lift`
-    used_symbols = collect_symbol_refs(stencil)
-    # do not extract when the stencil is capturing
-    if used_symbols:
+@dataclasses.dataclass(frozen=True)
+class TemporaryExtractionPredicate:
+    """
+    Construct a callable that determines if a lift expr can and should be extracted to a temporary.
+
+    The class optionally takes a heuristic that can restrict the extraction.
+    """
+
+    heuristics: Optional[Callable[[ir.Expr], bool]] = None
+
+    def __call__(self, expr: ir.Expr, num_occurences: int) -> bool:
+        """Determine if `expr` is an applied lift that should be extracted as a temporary."""
+        if not is_applied_lift(expr):
+            return False
+        # do not extract when the result is a list (i.e. a lift expression used in a `reduce` call)
+        # as we can not create temporaries for these stencils
+        if isinstance(expr.annex.type.dtype, type_inference.List):
+            return False
+        if self.heuristics and not self.heuristics(expr):
+            return False
+        stencil = expr.fun.args[0]  # type: ignore[attr-defined] # ensured by `is_applied_lift`
+        # do not extract when the stencil is capturing
+        used_symbols = collect_symbol_refs(stencil)
+        if used_symbols:
+            return False
+        return True
+
+
+@dataclasses.dataclass(frozen=True)
+class SimpleTemporaryExtractionHeuristics:
+    """
+    Heuristic that extracts only if a lift expr is derefed in more than one position.
+
+    Note that such expression result in redundant computations if inlined instead of being
+    placed into a temporary.
+    """
+
+    closure: ir.StencilClosure
+
+    @functools.cached_property
+    def closure_shifts(self):
+        return trace_shifts.TraceShifts.apply(self.closure, inputs_only=False)
+
+    def __call__(self, expr: ir.Expr) -> bool:
+        shifts = self.closure_shifts[id(expr)]
+        if len(shifts) > 1:
+            return True
         return False
-    return True
 
 
 def _closure_parameter_argument_mapping(closure: ir.StencilClosure):
@@ -193,7 +227,14 @@ def _ensure_expr_does_not_capture(expr: ir.Expr, whitelist: list[ir.Sym]) -> Non
     assert not (set(used_symbol_refs) - {param.id for param in whitelist})
 
 
-def split_closures(node: ir.FencilDefinition, offset_provider) -> FencilWithTemporaries:
+def split_closures(
+    node: ir.FencilDefinition,
+    offset_provider,
+    *,
+    extraction_heuristics: Optional[
+        Callable[[ir.StencilClosure], Callable[[ir.Expr], bool]]
+    ] = None,
+) -> FencilWithTemporaries:
     """Split closures on lifted function calls and introduce new temporary buffers for return values.
 
     Newly introduced temporaries will have the symbolic size of `AUTO_DOMAIN`. A symbol with the
@@ -205,6 +246,13 @@ def split_closures(node: ir.FencilDefinition, offset_provider) -> FencilWithTemp
     3. Extract lifted function class as new closures with the previously created temporary as output.
     The closures are processed in reverse order to properly respect the dependencies.
     """
+    if not extraction_heuristics:
+        # extract all (eligible) lifts
+        def always_extract_heuristics(_):
+            return lambda _: True
+
+        extraction_heuristics = always_extract_heuristics
+
     uid_gen_tmps = UIDGenerator(prefix="_tmp")
 
     type_inference.infer_all(node, offset_provider=offset_provider, save_to_annex=True)
@@ -228,9 +276,13 @@ def split_closures(node: ir.FencilDefinition, offset_provider) -> FencilWithTemp
                 current_closure.stencil if not is_scan else current_closure.stencil.args[0]  # type: ignore[attr-defined]  # ensured by is_scan
             )
 
+            extraction_predicate = TemporaryExtractionPredicate(
+                extraction_heuristics(current_closure)
+            )
+
             stencil_body, extracted_lifts, _ = extract_subexpression(
                 current_closure_stencil.expr,
-                temporary_extraction_predicate,
+                extraction_predicate,
                 uid_gen_tmps,
                 once_only=True,
                 deepest_expr_first=True,
@@ -454,7 +506,12 @@ def update_domains(
         if closure.domain == AUTO_DOMAIN:
             # every closure with auto domain should have a single out field
             assert isinstance(closure.output, ir.SymRef)
+
+            if closure.output.id not in domains:
+                raise NotImplementedError(f"Closure output '{closure.output.id}' is never used.")
+
             domain = domains[closure.output.id]
+
             closure = ir.StencilClosure(
                 domain=copy.deepcopy(domain),
                 stencil=closure.stencil,
@@ -467,14 +524,6 @@ def update_domains(
 
         closures.append(closure)
 
-        if closure.stencil == ir.SymRef(id="deref"):
-            # all closure inputs inherit the domain
-            for input_arg in _tuple_constituents(closure.inputs[0]):
-                assert isinstance(input_arg, ir.SymRef)
-                assert domains.get(input_arg.id, domain) == domain
-                domains[input_arg.id] = domain
-            continue
-
         local_shifts = trace_shifts.TraceShifts.apply(closure)
         for param, shift_chains in local_shifts.items():
             assert isinstance(param, str)
@@ -512,13 +561,22 @@ def update_domains(
                             (axis, range_) if axis != old_axis else (new_axis, new_range)
                             for axis, range_ in consumed_domain.ranges.items()
                         )
+                        # TODO(tehrengruber): Revisit. Somehow the order matters so preserve it.
+                        consumed_domain.ranges = dict(
+                            (axis, range_) if axis != old_axis else (new_axis, new_range)
+                            for axis, range_ in consumed_domain.ranges.items()
+                        )
                     else:
-                        raise NotImplementedError
+                        raise NotImplementedError()
                 consumed_domains.append(consumed_domain)
 
             # compute the bounds of all consumed domains
             if consumed_domains:
-                domains[param] = domain_union(consumed_domains).as_expr()
+                if all(
+                    consumed_domain.ranges.keys() == consumed_domains[0].ranges.keys()
+                    for consumed_domain in consumed_domains
+                ):  # scalar otherwise
+                    domains[param] = domain_union(consumed_domains).as_expr()
 
     return FencilWithTemporaries(
         fencil=ir.FencilDefinition(
@@ -597,10 +655,15 @@ def visit_FencilDefinition(
         node: ir.FencilDefinition,
         *,
         offset_provider: Mapping[str, Any],
+        extraction_heuristics: Optional[
+            Callable[[ir.StencilClosure], Callable[[ir.Expr], bool]]
+        ] = None,
         symbolic_sizes: Optional[dict[str, str]],
     ) -> FencilWithTemporaries:
         # Split closures on lifted function calls and introduce temporaries
-        res = split_closures(node, offset_provider=offset_provider)
+        res = split_closures(
+            node, offset_provider=offset_provider, extraction_heuristics=extraction_heuristics
+        )
         # Prune unreferences closure inputs introduced in the previous step
         res = PruneClosureInputs().visit(res)
         # Prune unused temporaries possibly introduced in the previous step
diff --git a/src/gt4py/next/iterator/transforms/pass_manager.py b/src/gt4py/next/iterator/transforms/pass_manager.py
index 08897861c2..fe14a8f580 100644
--- a/src/gt4py/next/iterator/transforms/pass_manager.py
+++ b/src/gt4py/next/iterator/transforms/pass_manager.py
@@ -13,7 +13,7 @@
 # SPDX-License-Identifier: GPL-3.0-or-later
 
 import enum
-from typing import Optional
+from typing import Callable, Optional
 
 from gt4py.next.iterator import ir
 from gt4py.next.iterator.transforms import simple_inline_heuristic
@@ -51,8 +51,6 @@ def _inline_lifts(ir, lift_mode):
         return InlineLifts(
             flags=InlineLifts.Flag.INLINE_TRIVIAL_DEREF_LIFT
             | InlineLifts.Flag.INLINE_DEREF_LIFT  # some tuple exprs found in FVM don't work yet.
-            | InlineLifts.Flag.INLINE_LIFTED_ARGS
-            # needed for UnrollReduce and lift args like `(↑(λ() → constant)`
         ).visit(ir)
     else:
         raise ValueError()
@@ -73,6 +71,8 @@ def _inline_into_scan(ir, *, max_iter=10):
     return ir
 
 
+# TODO(tehrengruber): Revisit interface to configure temporary extraction. We currently forward
+#  `lift_mode` and `temporary_extraction_heuristics` which is inconvenient.
 def apply_common_transforms(
     ir: ir.Node,
     *,
@@ -82,6 +82,9 @@ def apply_common_transforms(
     common_subexpression_elimination=True,
     force_inline_lambda_args=False,
     unconditionally_collapse_tuples=False,
+    temporary_extraction_heuristics: Optional[
+        Callable[[ir.StencilClosure], Callable[[ir.Expr], bool]]
+    ] = None,
     symbolic_domain_sizes: Optional[dict[str, str]] = None,
 ):
     if lift_mode is None:
@@ -121,6 +124,33 @@ def apply_common_transforms(
     else:
         raise RuntimeError("Inlining 'lift' and 'lambdas' did not converge.")
 
+    if lift_mode != LiftMode.FORCE_INLINE:
+        assert offset_provider is not None
+        ir = CreateGlobalTmps().visit(
+            ir,
+            offset_provider=offset_provider,
+            extraction_heuristics=temporary_extraction_heuristics,
+            symbolic_sizes=symbolic_domain_sizes,
+        )
+
+        for _ in range(10):
+            inlined = InlineLifts().visit(ir)
+            inlined = InlineLambdas.apply(
+                inlined,
+                opcount_preserving=True,
+                force_inline_lift_args=True,
+            )
+            if inlined == ir:
+                break
+            ir = inlined
+        else:
+            raise RuntimeError("Inlining 'lift' and 'lambdas' did not converge.")
+
+        # If after creating temporaries, the scan is not at the top, we inline.
+        # The following example doesn't have a lift around the shift, i.e. temporary pass will not extract it.
+        # λ(inp) → scan(λ(state, k, kp) → state + ·k + ·kp, True, 0.0)(inp, ⟪Koffₒ, 1ₒ⟫(inp))`
+        ir = _inline_into_scan(ir)
+
     # Since `CollapseTuple` relies on the type inference which does not support returning tuples
     # larger than the number of closure outputs as given by the unconditional collapse, we can
     # only run the unconditional version here instead of in the loop above.
@@ -134,6 +164,7 @@ def apply_common_transforms(
 
     ir = FuseMaps().visit(ir)
     ir = CollapseListGet().visit(ir)
+
     if unroll_reduce:
         for _ in range(10):
             unrolled = UnrollReduce.apply(ir, offset_provider=offset_provider)
@@ -142,22 +173,11 @@ def apply_common_transforms(
             ir = unrolled
             ir = CollapseListGet().visit(ir)
             ir = NormalizeShifts().visit(ir)
-            ir = _inline_lifts(ir, lift_mode)
+            ir = _inline_lifts(ir, LiftMode.FORCE_INLINE)
             ir = NormalizeShifts().visit(ir)
         else:
             raise RuntimeError("Reduction unrolling failed.")
 
-    if lift_mode != LiftMode.FORCE_INLINE:
-        assert offset_provider is not None
-        ir = CreateGlobalTmps().visit(
-            ir, offset_provider=offset_provider, symbolic_sizes=symbolic_domain_sizes
-        )
-        ir = InlineLifts().visit(ir)
-        # If after creating temporaries, the scan is not at the top, we inline.
-        # The following example doesn't have a lift around the shift, i.e. temporary pass will not extract it.
-        # λ(inp) → scan(λ(state, k, kp) → state + ·k + ·kp, True, 0.0)(inp, ⟪Koffₒ, 1ₒ⟫(inp))`
-        ir = _inline_into_scan(ir)
-
     ir = EtaReduction().visit(ir)
     ir = ScanEtaReduction().visit(ir)
 
diff --git a/src/gt4py/next/iterator/type_inference.py b/src/gt4py/next/iterator/type_inference.py
index d65f67b266..683a57561c 100644
--- a/src/gt4py/next/iterator/type_inference.py
+++ b/src/gt4py/next/iterator/type_inference.py
@@ -21,6 +21,7 @@
 import gt4py.next as gtx
 from gt4py.next.common import Connectivity
 from gt4py.next.iterator import ir
+from gt4py.next.iterator.transforms.global_tmps import FencilWithTemporaries
 from gt4py.next.type_inference import Type, TypeVar, freshen, reindex_vars, unify
 
 
@@ -936,6 +937,9 @@ def visit_StencilClosure(
         )
         return Closure(output=output, inputs=Tuple.from_elems(*inputs))
 
+    def visit_FencilWithTemporaries(self, node: FencilWithTemporaries, **kwargs):
+        return self.visit(node.fencil, **kwargs)
+
     def visit_FencilDefinition(
         self,
         node: ir.FencilDefinition,
diff --git a/src/gt4py/next/program_processors/codegens/gtfn/gtfn_module.py b/src/gt4py/next/program_processors/codegens/gtfn/gtfn_module.py
index 718fef72af..c157cdcc46 100644
--- a/src/gt4py/next/program_processors/codegens/gtfn/gtfn_module.py
+++ b/src/gt4py/next/program_processors/codegens/gtfn/gtfn_module.py
@@ -17,7 +17,7 @@
 import dataclasses
 import functools
 import warnings
-from typing import Any, Final, Optional
+from typing import Any, Callable, Final, Optional
 
 import numpy as np
 
@@ -58,6 +58,9 @@ class GTFNTranslationStep(
     lift_mode: Optional[LiftMode] = None
     device_type: core_defs.DeviceType = core_defs.DeviceType.CPU
     symbolic_domain_sizes: Optional[dict[str, str]] = None
+    temporary_extraction_heuristics: Optional[
+        Callable[[itir.StencilClosure], Callable[[itir.Expr], bool]]
+    ] = None
 
     def _default_language_settings(self) -> languages.LanguageWithHeaderFilesSettings:
         match self.device_type:
@@ -179,14 +182,14 @@ def _preprocess_program(
         self,
         program: itir.FencilDefinition,
         offset_provider: dict[str, Connectivity | Dimension],
-        runtime_lift_mode: Optional[LiftMode] = None,
+        runtime_lift_mode: Optional[LiftMode],
     ) -> itir.FencilDefinition:
         # TODO(tehrengruber): Remove `lift_mode` from call interface. It has been implicitly added
         #  to the interface of all (or at least all of concern) backends, but instead should be
         #  configured in the backend itself (like it is here), until then we respect the argument
         #  here and warn the user if it differs from the one configured.
         lift_mode = runtime_lift_mode or self.lift_mode
-        if lift_mode != self.lift_mode:
+        if runtime_lift_mode and runtime_lift_mode != self.lift_mode:
             warnings.warn(
                 f"GTFN Backend was configured for LiftMode `{str(self.lift_mode)}`, but "
                 f"overriden to be {str(runtime_lift_mode)} at runtime."
@@ -202,6 +205,7 @@ def _preprocess_program(
             # sid::composite (via hymap) supports assigning from tuple with more elements to tuple with fewer elements
             unconditionally_collapse_tuples=True,
             symbolic_domain_sizes=self.symbolic_domain_sizes,
+            temporary_extraction_heuristics=self.temporary_extraction_heuristics,
         )
 
         new_program = apply_common_transforms(
diff --git a/src/gt4py/next/program_processors/runners/gtfn.py b/src/gt4py/next/program_processors/runners/gtfn.py
index baa45ddc0e..157c00c368 100644
--- a/src/gt4py/next/program_processors/runners/gtfn.py
+++ b/src/gt4py/next/program_processors/runners/gtfn.py
@@ -22,7 +22,7 @@
 import gt4py.next.allocators as next_allocators
 from gt4py.eve.utils import content_hash
 from gt4py.next import common
-from gt4py.next.iterator.transforms import LiftMode
+from gt4py.next.iterator.transforms import LiftMode, global_tmps
 from gt4py.next.otf import languages, recipes, stages, step_types, workflow
 from gt4py.next.otf.binding import nanobind
 from gt4py.next.otf.compilation import cache, compiler
@@ -187,7 +187,8 @@ def compilation_hash(otf_closure: stages.ProgramCall) -> int:
         name="run_gtfn_with_temporaries",
         otf_workflow=gtfn_executor.otf_workflow.replace(
             translation=gtfn_executor.otf_workflow.translation.replace(
-                lift_mode=LiftMode.FORCE_TEMPORARIES
+                lift_mode=LiftMode.FORCE_TEMPORARIES,
+                temporary_extraction_heuristics=global_tmps.SimpleTemporaryExtractionHeuristics,
             ),
         ),
     ),
diff --git a/tests/next_tests/integration_tests/feature_tests/ffront_tests/test_execution.py b/tests/next_tests/integration_tests/feature_tests/ffront_tests/test_execution.py
index 7fc2d82e67..ae5e434085 100644
--- a/tests/next_tests/integration_tests/feature_tests/ffront_tests/test_execution.py
+++ b/tests/next_tests/integration_tests/feature_tests/ffront_tests/test_execution.py
@@ -622,7 +622,7 @@ def simple_scan_operator(carry: float) -> float:
 @pytest.mark.uses_lift_expressions
 @pytest.mark.uses_scan_nested
 def test_solve_triag(cartesian_case):
-    if cartesian_case.executor == gtfn.run_gtfn_with_temporaries:
+    if cartesian_case.executor == gtfn.run_gtfn_with_temporaries.executor:
         pytest.xfail("Temporary extraction does not work correctly in combination with scans.")
 
     @gtx.scan_operator(axis=KDim, forward=True, init=(0.0, 0.0))
diff --git a/tests/next_tests/unit_tests/iterator_tests/transforms_tests/test_global_tmps.py b/tests/next_tests/unit_tests/iterator_tests/transforms_tests/test_global_tmps.py
index 5c2802f90c..46ca02217f 100644
--- a/tests/next_tests/unit_tests/iterator_tests/transforms_tests/test_global_tmps.py
+++ b/tests/next_tests/unit_tests/iterator_tests/transforms_tests/test_global_tmps.py
@@ -20,6 +20,7 @@
 from gt4py.next.iterator.transforms.global_tmps import (
     AUTO_DOMAIN,
     FencilWithTemporaries,
+    SimpleTemporaryExtractionHeuristics,
     Temporary,
     collect_tmps_info,
     split_closures,
@@ -32,53 +33,23 @@ def test_split_closures():
     testee = ir.FencilDefinition(
         id="f",
         function_definitions=[],
-        params=[ir.Sym(id="d"), ir.Sym(id="inp"), ir.Sym(id="out")],
+        params=[im.sym("d"), im.sym("inp"), im.sym("out")],
         closures=[
             ir.StencilClosure(
-                domain=ir.FunCall(fun=ir.SymRef(id="cartesian_domain"), args=[]),
-                stencil=ir.Lambda(
-                    params=[ir.Sym(id="baz_inp")],
-                    expr=ir.FunCall(
-                        fun=ir.SymRef(id="deref"),
-                        args=[
-                            ir.FunCall(
-                                fun=ir.FunCall(
-                                    fun=ir.SymRef(id="lift"),
-                                    args=[
-                                        ir.Lambda(
-                                            params=[ir.Sym(id="bar_inp")],
-                                            expr=ir.FunCall(
-                                                fun=ir.SymRef(id="deref"),
-                                                args=[
-                                                    ir.FunCall(
-                                                        fun=ir.FunCall(
-                                                            fun=ir.SymRef(id="lift"),
-                                                            args=[
-                                                                ir.Lambda(
-                                                                    params=[ir.Sym(id="foo_inp")],
-                                                                    expr=ir.FunCall(
-                                                                        fun=ir.SymRef(id="deref"),
-                                                                        args=[
-                                                                            ir.SymRef(id="foo_inp")
-                                                                        ],
-                                                                    ),
-                                                                )
-                                                            ],
-                                                        ),
-                                                        args=[ir.SymRef(id="bar_inp")],
-                                                    )
-                                                ],
-                                            ),
-                                        )
-                                    ],
-                                ),
-                                args=[ir.SymRef(id="baz_inp")],
+                domain=im.call("cartesian_domain")(),
+                stencil=im.lambda_("baz_inp")(
+                    im.deref(
+                        im.lift(
+                            im.lambda_("bar_inp")(
+                                im.deref(
+                                    im.lift(im.lambda_("foo_inp")(im.deref("foo_inp")))("bar_inp")
+                                )
                             )
-                        ],
-                    ),
+                        )("baz_inp")
+                    )
                 ),
-                output=ir.SymRef(id="out"),
-                inputs=[ir.SymRef(id="inp")],
+                output=im.ref("out"),
+                inputs=[im.ref("inp")],
             )
         ],
     )
@@ -87,54 +58,31 @@ def test_split_closures():
         id="f",
         function_definitions=[],
         params=[
-            ir.Sym(id="d"),
-            ir.Sym(id="inp"),
-            ir.Sym(id="out"),
-            ir.Sym(id="_tmp_1"),
-            ir.Sym(id="_tmp_2"),
-            ir.Sym(id="_gtmp_auto_domain"),
+            im.sym("d"),
+            im.sym("inp"),
+            im.sym("out"),
+            im.sym("_tmp_1"),
+            im.sym("_tmp_2"),
+            im.sym("_gtmp_auto_domain"),
         ],
         closures=[
             ir.StencilClosure(
                 domain=AUTO_DOMAIN,
-                stencil=ir.Lambda(
-                    params=[ir.Sym(id="foo_inp")],
-                    expr=ir.FunCall(
-                        fun=ir.SymRef(id="deref"),
-                        args=[ir.SymRef(id="foo_inp")],
-                    ),
-                ),
-                output=ir.SymRef(id="_tmp_2"),
-                inputs=[ir.SymRef(id="inp")],
+                stencil=im.lambda_("foo_inp")(im.deref("foo_inp")),
+                output=im.ref("_tmp_2"),
+                inputs=[im.ref("inp")],
             ),
             ir.StencilClosure(
                 domain=AUTO_DOMAIN,
-                stencil=ir.Lambda(
-                    params=[
-                        ir.Sym(id="bar_inp"),
-                        ir.Sym(id="_tmp_2"),
-                    ],
-                    expr=ir.FunCall(
-                        fun=ir.SymRef(id="deref"),
-                        args=[
-                            ir.SymRef(id="_tmp_2"),
-                        ],
-                    ),
-                ),
-                output=ir.SymRef(id="_tmp_1"),
-                inputs=[ir.SymRef(id="inp"), ir.SymRef(id="_tmp_2")],
+                stencil=im.lambda_("bar_inp", "_tmp_2")(im.deref("_tmp_2")),
+                output=im.ref("_tmp_1"),
+                inputs=[im.ref("inp"), im.ref("_tmp_2")],
             ),
             ir.StencilClosure(
-                domain=ir.FunCall(fun=ir.SymRef(id="cartesian_domain"), args=[]),
-                stencil=ir.Lambda(
-                    params=[ir.Sym(id="baz_inp"), ir.Sym(id="_tmp_1")],
-                    expr=ir.FunCall(
-                        fun=ir.SymRef(id="deref"),
-                        args=[ir.SymRef(id="_tmp_1")],
-                    ),
-                ),
-                output=ir.SymRef(id="out"),
-                inputs=[ir.SymRef(id="inp"), ir.SymRef(id="_tmp_1")],
+                domain=im.call("cartesian_domain")(),
+                stencil=im.lambda_("baz_inp", "_tmp_1")(im.deref("_tmp_1")),
+                output=im.ref("out"),
+                inputs=[im.ref("inp"), im.ref("_tmp_1")],
             ),
         ],
     )
@@ -143,6 +91,60 @@ def test_split_closures():
     assert actual.fencil == expected
 
 
+def test_split_closures_simple_heuristics():
+    UIDs.reset_sequence()
+    testee = ir.FencilDefinition(
+        id="f",
+        function_definitions=[],
+        params=[im.sym("d"), im.sym("inp"), im.sym("out")],
+        closures=[
+            ir.StencilClosure(
+                domain=im.call("cartesian_domain")(),
+                stencil=im.lambda_("foo")(
+                    im.let("lifted_it", im.lift(im.lambda_("bar")(im.deref("bar")))("foo"))(
+                        im.plus(im.deref("lifted_it"), im.deref(im.shift("I", 1)("lifted_it")))
+                    )
+                ),
+                output=im.ref("out"),
+                inputs=[im.ref("inp")],
+            )
+        ],
+    )
+
+    expected = ir.FencilDefinition(
+        id="f",
+        function_definitions=[],
+        params=[
+            im.sym("d"),
+            im.sym("inp"),
+            im.sym("out"),
+            im.sym("_tmp_1"),
+            im.sym("_gtmp_auto_domain"),
+        ],
+        closures=[
+            ir.StencilClosure(
+                domain=AUTO_DOMAIN,
+                stencil=im.lambda_("bar")(im.deref("bar")),
+                output=im.ref("_tmp_1"),
+                inputs=[im.ref("inp")],
+            ),
+            ir.StencilClosure(
+                domain=im.call("cartesian_domain")(),
+                stencil=im.lambda_("foo", "_tmp_1")(
+                    im.plus(im.deref("_tmp_1"), im.deref(im.shift("I", 1)("_tmp_1")))
+                ),
+                output=im.ref("out"),
+                inputs=[im.ref("inp"), im.ref("_tmp_1")],
+            ),
+        ],
+    )
+    actual = split_closures(
+        testee, extraction_heuristics=SimpleTemporaryExtractionHeuristics, offset_provider={}
+    )
+    assert actual.tmps == [Temporary(id="_tmp_1")]
+    assert actual.fencil == expected
+
+
 def test_split_closures_lifted_scan():
     UIDs.reset_sequence()