A system for supplying turbine cooling air flow includes a turbofan engine, a heat exchanger, and a door. The turbofan engine includes an engine case that has an inner volume within which at least a gas turbine engine is mounted, and a bypass flow passage that is defined by an outer fan duct and an inner fan duct and that is configured to direct fan air flow therethrough. The heat exchanger is disposed within the turbofan engine, is coupled to receive fluid and cooling air from the bypass flow passage, and is configured to transfer heat between fluid and the cooling air. The door is movably mounted in the turbofan engine and is movable between a closed position, in which the cooling air will not flow through the heat exchanger, and an open position, in which the cooling air may flow through the heat exchanger.