A gas turbine engine according to an exemplary embodiment of this disclosure includes, among other possible things, a compressor section including an aft most exit, an air tap configured to draw air from a point upstream of the aft most exit, an auxiliary compressor configured to receive air from the air tap and discharge air to a turbine section, an electric motor configured to drive the auxiliary compressor, a first heat exchanger within an inlet passage between the air tap and an inlet to the auxiliary compressor, and a second heat exchanger disposed within an outlet passage between an outlet of the auxiliary compressor and the turbine section.