On a hot day a friend suggests that you can make your kitchen cooler by leaving the refrigerator door open. Would leaving the refrigerator door open cause the air temperature in the kitchen to decrease?
No (in fact the room temperature would increase slightly)
...see note below for possible exception
A refrigerator acts as a "heat pump" moving energy in the form of heat from the inside of the refrigerator to the compressor coils on the outside of the refrigerator. On old refrigerators the compressor coils were exposed on the outside back and it was easy to check that they did indeed become very warm; in modern refrigerators these coils are enclosed but still outside of the insulated refrigerator interior.
The motor required to run the compressor pump will actually generate some additional heat, so the total heat in the room will actually increase.
A possible exception might occur if you could place the compressor coils outside of the room (e.g. outdoors).