A gas turbine engine includes a turbine rotor connected to a main compressor rotor. A tail cone is mounted inward of an exhaust core flow. A generator rotor is adjacent a generator stator. The generator rotor and stator are mounted within the tail cone. A passage connects a bypass flow path to the tail cone. A cooling air compressor is operable within the passage. The turbine rotor drives a shaft to drive the generator rotor and the cooling compressor. A method is also disclosed.