Comment by jdranczewski

You can, but the heat needs to go somewhere, and now you're back to square one, with "how do I get rid of all this heat". Earth refrigerators have a large heat exchanger on the back for this purpose. In fact now you need to get rid of both of the heat your compute generates and the energy your refrigerator pump uses - an example people often give is that a fridge with an open door actually heats the room, as it spends energy on moving heat around pointlessly.