Abstract: In a vehicle equipped with an air conditioning system (1) including a heat exchanger for heating or cooling supply air to a cabin of the vehicle by heat exchange with heat transfer medium supplied from an accessory (6, 8) driven by a vehicle engine, a value relating to the capability of the heat transfer medium to heat or cool the supply air is detected, and the engine is automatically stopped for a predetermined period when the vehicle is stopping, the air conditioning system (1) is in operation and the detected value meets a specified condition (a condition that the engine cooling water temperature is equal to or higher than a specified temperature).