It sounds too good to be true to have a refrigerator that generates energy, but I lack the education in quantum physics to understand why it would be unreasonable or impossible.
The peltier or Seebeck effect does just this. By heating one side of the element and cooling the other, you get a small amount of electricity. It's impractical and very inefficient, though.
Because you must cool one side, you have to have some sort of system to remove heat as quickly as you put it in. Active cooling with a fan requires too much energy, so you're left with passive cooling. As well, the amount of power you get goes down as the cold side gets hotter.
There are plenty of good uses, though. Old gas water heaters actually used an electronic circuit to control the gas. A thermocouple is placed above the pilot light and creates enough energy to trigger the solenoid valve. Many types of temperature sensors work in the same way.