A system and method for adaptively controlling a cooldown cycle of an auxiliary power unit (APU) that is operating and rotating at a rotational speed includes reducing the rotational speed of the APU to a predetermined cooldown speed magnitude that ensures combustor inlet temperature has reached a predetermined temperature value, determining, based on one or more of operational parameters of the APU, when a lean blowout of the APU is either imminent or has occurred, and when a lean blowout is imminent or has occurred, varying one or more parameters associated with the shutdown/cooldown cycle.