In a gas turbine engine having a rim cavity formed between a rotor disk and a stator, and a brush seal or other seal member providing an airflow seal between the stator and a side plate of the rotor disk, a thermally responsive valve device is located in the bypass passage of the stator to form a parallel air flow path with the brush seal. As the brush seal wears and the leakage airflow around the worn brush seal increases, the air flow temperature in the rim cavity would decrease. The thermally responsive valve device would detect the decreasing airflow temperature, and reduce the airflow passing through the bypass passage in order to prevent the temperature of the rim cavity from decreasing. The temperature responsive valve device makes use of a bimetallic valve member that regulates airflow based upon temperature.