A gas turbine engine includes a buffer cooling system having a first heat exchanger, a first passageway, a second passageway and a third passageway. The first heat exchanger exchanges heat with a bleed airflow to provide a conditioned airflow. The first passageway communicates a first portion of the conditioned airflow to a high pressure compressor of the gas turbine engine, the second passageway communicates a second portion of the conditioned airflow to a high pressure turbine of the gas turbine engine, and the third passageway communicates a third portion of the conditioned airflow to a low pressure turbine of the gas turbine engine.