Running it from inside a refrigerator is a no-go I think. Once I close the lid on that thing, it will be isolated from the rest of the environment in the refrigerator. Whatever heat is produced inside the chamber, the cold from the outside will not penetrate.
I just called up an electro engineer friend of mine and told him about my suggestion. 1. Drill a hole in each side of the centrifuge, 2. insert plastic tubing with the exact diameter of the hole, 3. attach a blowing fan to a peltier-cooled block, 4. attach thermostat inside chamber, and have it regulate the fan speed.
That way I can have the fan blow a steady stream of cold air through the chamber of the centrifuge, and the thermostat will lower or increase the fan speed depending on the chamber temperature.
However - how accurate must the temperature be? Exactly 4 C? or can it be like.. from +1 C to + 6 C?