A thermal management system for a gas turbine engine includes a high pressure compressor rotor having a plurality of disks and a shaft; at least one forward cavity between a rim of at least one of the disks and the shaft and at least one aft cavity formed between a rim of at least one other of the disks and the shaft; a first flow of cooling air in the at least one forward cavity; and a second flow of cooling air in the at least one aft cavity.