An aircraft support pylon designed to attach a turbomachine housed in a nacelle to an aircraft fuselage is disclosed. The pylon includes a cooler, located substantially in the vicinity of a leading edge of the pylon, and able to be heated by a hot fluid, the hot fluid intended to be cooled by heat exchange with cold air outside the cooler. The pylon also includes at least one air evacuation duct, at the exit from the cooler and extending longitudinally in an internal volume of the pylon to a trailing edge of the pylon.