There is a difference between hot food and a hot chunk of metal.
The radiator will alwys pump about the same amount of heat out (not technically right, but close)
The food isn't a constant source of heat, once it gets cold, it isn't hot anymore
Now the radiator may never get cold because a fridge isn't designed to cope with constant heat. Its probably made to cool down stuff that is hot or warm, like pop cans etc. pop cans don't produce heat by themselves.
If you get a high enough capacity fridge, itmight work