diff --git a/airflow-core/src/airflow/jobs/scheduler_job_runner.py b/airflow-core/src/airflow/jobs/scheduler_job_runner.py
index 7e92ab3120a34..fa771eeb9999a 100644
--- a/airflow-core/src/airflow/jobs/scheduler_job_runner.py
+++ b/airflow-core/src/airflow/jobs/scheduler_job_runner.py
@@ -3494,6 +3494,7 @@ def _purge_task_instances_without_heartbeats(
                 request,
             )
             self.executor.send_callback(request)
+            ti.handle_failure(error=str(task_instance_heartbeat_timeout_message_details), session=session)
             executor = self._try_to_load_executor(
                 ti, session, team_name=dag_id_to_team_name.get(ti.dag_id, NOTSET)
             )
diff --git a/airflow-core/tests/unit/jobs/test_scheduler_job.py b/airflow-core/tests/unit/jobs/test_scheduler_job.py
index 67986c0297ee4..76bfabda2b17a 100644
--- a/airflow-core/tests/unit/jobs/test_scheduler_job.py
+++ b/airflow-core/tests/unit/jobs/test_scheduler_job.py
@@ -8308,6 +8308,38 @@ def test_scheduler_passes_context_from_server_on_heartbeat_timeout(self, dag_mak
         assert callback_request.context_from_server.dag_run.logical_date == dag_run.logical_date
         assert callback_request.context_from_server.max_tries == ti.max_tries
 
+    def test_heartbeat_timeout_converges_ti_state_before_next_scan(self, dag_maker, session):
+        """A heartbeat-timed-out TI should not be found again on the next scheduler scan."""
+        with dag_maker(dag_id="test_heartbeat_timeout_dedupe", session=session):
+            EmptyOperator(task_id="test_task", on_failure_callback=lambda context: None)
+
+        dag_run = dag_maker.create_dagrun(run_id="test_run", state=DagRunState.RUNNING)
+
+        mock_executor = MagicMock()
+        scheduler_job = Job()
+        self.job_runner = SchedulerJobRunner(scheduler_job, executors=[mock_executor])
+
+        ti = dag_run.get_task_instance(task_id="test_task")
+        ti.state = TaskInstanceState.RUNNING
+        ti.try_number = 1
+        ti.max_tries = 0
+        ti.queued_by_job_id = scheduler_job.id
+        ti.start_date = timezone.utcnow() - timedelta(seconds=900)
+        ti.last_heartbeat_at = timezone.utcnow() - timedelta(seconds=600)
+        session.merge(ti)
+        session.commit()
+
+        self.job_runner._find_and_purge_task_instances_without_heartbeats()
+
+        session.expire_all()
+        ti.refresh_from_db(session=session)
+        assert ti.state != TaskInstanceState.RUNNING
+        assert self.job_runner._find_task_instances_without_heartbeats(session=session) == []
+
+        self.job_runner._find_and_purge_task_instances_without_heartbeats()
+
+        mock_executor.send_callback.assert_called_once()
+
     @pytest.mark.parametrize(
         ("retries", "callback_kind", "expected"),
         [