In an aircraft including a gas turbine engine having a compressor including a compressor booster, a turbine, and a nacelle, a system for cooling compressor discharge air provided to the turbine to cool the turbine includes a heat exchanger provided in a nacelle compartment of the gas turbine engine configured to cool the compressor discharge air by exchanging heat from the compressor discharge air to a cooling fluid; and a cooling fluid circuit configured to circulate cooling fluid through the heat exchanger and a heat sink, wherein the heat sink is at least one of an inlet of the nacelle compartment, an inlet of the compressor booster, or outlet guide vanes of the gas turbine engine.