I think that one of the problems with this idea is that the motor on the refrigerator can't cope with the constant heat produced by the computer...it's designed for something that will stay relatively cool once you cool it, not something that will heat up even when you do cool it.
Now, I'm not positive that this is the case, so I would look into finding someone who has been successful with this, and has been for more than a couple of months or so...as the motor might just not ever shut off, and that would probably wear it out a bit, don't you think?