A gas turbine engine section includes a plurality of spaced rotor stages, with a static guide vane intermediate the spaced rotor stages. The static guide vane provides swirl into air passing toward a downstream one of the spaced rotor stages, and an outer housing surrounding the spaced rotor stages. A diverter diverts a portion of air radially outwardly through the outer housing, and across at least one heat exchanger. The diverted air passes back into a duct radially inwardly through the outer housing, and is exhausted toward the downstream one of the spaced rotor stages.