Can a room be cooled by leaving the door of an electric refrigerator open in a closed room?

A refrigerator is a heat engine which works in opposite to other heat engines like petrol engine and diesel engine. Thus, a refrigerator extracts heat from the freezing chamber, some work is done on it by electric motor and rejects heat into the surrounding air, thus warming the air. Therefore if the door of a running refrigerator is left open, the room will not be cooled down but instead heated slightly.