A prediction element predicts a predicted arrival time at a destination based on a travel route found by a search element. In normal control mode, the first learning element learns the time period from the time point at which a vehicle is stopped, until an air-based on the predicted arrival time and the result of the learning, a control element estimates a linger period from the present moment until the passenger leaves the passenger compartment after arrival, and, based on the temperatures inside the passenger compartment and the outside as detected by first and second temperature detection element and temperature transition time information, specifies a divergence period from stopping the air-conditioning device until the temperature inside the passenger compartment leaves a comfortable temperature range. The control element stops the air-conditioning device automatically when it is decided that the linger period has become not lager than the divergence period.