def METHOD_NAME(postgres_airflow_db: str) -> None:
    with tempfile.TemporaryDirectory() as dags_path:
        with open(os.path.join(dags_path, "dag.py"), "wb") as f:
            f.write(bytes(DAG_RUN_CONF_DAG.encode("utf-8")))
        airflow_db = make_persistent_airflow_db_resource(
            uri=postgres_airflow_db, dag_run_config={"configuration_key": "foo"}
        )
        definitions = make_dagster_definitions_from_airflow_dags_path(
            dags_path, resource_defs={"airflow_db": airflow_db}
        )
        job = definitions.get_job_def("dag_run_conf_dag")
        result = job.execute_in_process(
            tags={AIRFLOW_EXECUTION_DATE_STR: datetime.datetime(2023, 2, 2).isoformat()}
        )
        assert result.success
        assert Variable.get("CONFIGURATION_VALUE") == "foo"