A method of cooling a gas turbine engine case assembly includes moving a fan air valve that is operatively connected to a pre-cooler having a bypass inlet that is configured to receive bypass air that bypasses a gas turbine engine core to facilitate a provision of bypass air through a fan air valve inlet to the bypass inlet to a first open position, in response to a core compartment temperature being greater than a target core compartment temperature. The method further includes bleeding the bypass air through a bypass outlet of the pre-cooler into a core compartment.