What is the fate of the hot air used by a thermal anti-ice system after it has heated the aircraft surface?

The hot air used by a thermal anti-ice system is typically dumped overboard after it has heated the aircraft surface. This is because the primary function of the thermal anti-ice system is to prevent ice from forming on critical surfaces of the aircraft, such as wings and engine inlets, by circulating hot air. Once this hot air has served its purpose of providing heat to prevent ice accumulation, it is no longer needed for the anti-icing process.

The hot air is expelled overboard because keeping it for other purposes, such as recirculation, would not be efficient or effective. The design of thermal anti-ice systems generally does not incorporate mechanisms for rerouting the heated air back to the engine or storing it, as the primary concern is maintaining safe operation without ice buildup during flight.