A blower fan is driven, and conditioning air flows down through an evaporator and then is supplied into a vehicle compartment. An idling-stop condition in a roof-open state is set to make an idling stop to be relatively easily attained, compared to a roof-closed state, so that a fuel economy can be improved. When an outside-air temperature is a specified temperature or higher or a solar-radiation intensity is a specified degree or greater at an engine's automatic stop, the blower fan is driven, so that the conditioning air is supplied toward a passenger in a manner of an electric fan. The evaporator through which the conditioning air flows down is sufficiently cool at the timing right after the automatic stop of the engine. Accordingly, it is preferable to configure such that the sufficiently-cooled conditioning air is supplied for a properly-long period of time.