A method for cooling a jacketed autoclave or steam sterilizer by allowing a film of water to flow down as inner wall of the sterilizer's jacket. Condensate from the jacket space is drawn into a water ring pump. The water ring pump draws condensate from the lowest point of the jacket to a water side of the pump, and gas from the jacket to a normal suction inlet of the pump. During the process of cooling the sterilizer, a stream of water and air from the water ring pump is conducted to an upper part of the jacket of the steam sterilizer and is allowed to flow as a film down the inner wall of the jacket. Evaporation of the water is enhanced by lowering the pressure in the jacket.