System and method to exhaust spent cooling air of gas turbine engine active clearance control

An exemplary thermal air exhaust system includes circumferentially extending exhaust passages to exhaust thermal control air from an annular region between an outer casing and a distribution manifold encircling an axially extending portion of the casing after the thermal control air has been sprayed on at least one thermal control ring attached to the outer casing and/or onto the outer casing by spray tubes with spray holes. Baffles attached to base panels of the distribution manifold and contoured to form the exhaust passages between the baffles and base panels. The exhaust passages having exhaust passage inlets formed by radially facing exhaust holes through the baffles and exhaust passage outlets formed by circumferentially facing exhaust passage outlets between the baffles and the base panels. Thermal control air is sprayed on at least one thermal control ring and/or onto the outer casing and then circumferentially exhausted through the exhaust passages.