Expensive but possible: Two sets of Peltier heat modules:
You heat one side of set A by burning Propane or a by-product of oven/stove they produce electricity to run the B set to cool the fridge. Watch temperature limits!
Have seen big boys toys (wine coolers etc) and camping gear using these, in some case they are attached to a refrigerant spider to improve heat transfer. Though the cost to power ratio is high: and they are usually run at 12-15ºC - above safe food storage temperatures.
Also battery, solar, and water wheel compatible, very good for current CO2 global warning concerns.