A compressor section for use in a gas turbine engine comprises a compressor rotor having a hub and a plurality of blades extending radially outwardly from the hub and an outer housing surrounding an outer periphery of the blades. A tap taps air at a radially outer first location, passing the tapped air through a heat exchanger, and returning the tapped air to an outlet at a second location which is radially inward of the first location, to provide cooling air adjacent to the hub. A gas turbine engine is also disclosed.