diff --git a/cosmos/__init__.py b/cosmos/__init__.py
index c269dd545f..48a1cd7aee 100644
--- a/cosmos/__init__.py
+++ b/cosmos/__init__.py
@@ -9,7 +9,7 @@
 
 from cosmos import settings
 
-__version__ = "1.10.1"
+__version__ = "1.10.2a1"
 
 if not settings.enable_memory_optimised_imports:
     from cosmos.airflow.dag import DbtDag
diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 5062620417..a4c2098803 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -389,6 +389,9 @@ def store_freshness_json(self, tmp_project_dir: str, context: Context) -> None:
             self.freshness = ""
 
     def _override_rtif(self, context: Context) -> None:
+        if not self.should_store_compiled_sql:
+            return
+
         if AIRFLOW_VERSION.major == _AIRFLOW3_MAJOR_VERSION:
             self.overwrite_rtif_after_execution = True
             return
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index 9ba037631d..7c86e39bff 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -1920,3 +1920,34 @@ def test_delete_sql_files_no_remote_target_configured(mock_configure_remote):
     with patch.object(operator.log, "warning") as mock_log_warning:
         operator._delete_sql_files()
         mock_log_warning.assert_called_once_with(expected_log_message)
+
+
+@pytest.mark.skipif(version.parse(airflow_version).major == 3, reason="Test only applies to Airflow 2")
+def test_override_rtif_airflow2_with_should_store_compiled_sql_false():
+    """Test that _override_rtif does nothing in Airflow 2 when should_store_compiled_sql is False"""
+    operator = DbtRunLocalOperator(
+        task_id="test",
+        profile_config=None,
+        project_dir="my/dir",
+        should_store_compiled_sql=False,
+    )
+
+    context = {"task_instance": MagicMock()}
+
+    operator._override_rtif(context)
+    assert not context["task_instance"].called
+
+
+@pytest.mark.skipif(version.parse(airflow_version).major == 2, reason="Test only applies to Airflow 3")
+def test_override_rtif_airflow3_with_should_store_compiled_sql_false():
+    """Test that _override_rtif sets overwrite_rtif_after_execution to False in Airflow 3 when should_store_compiled_sql is False"""
+    operator = DbtRunLocalOperator(
+        task_id="test",
+        profile_config=None,
+        project_dir="my/dir",
+        should_store_compiled_sql=False,
+    )
+
+    context = {"task_instance": MagicMock()}
+    operator._override_rtif(context)
+    assert operator.overwrite_rtif_after_execution is False