It will work fine with a 12V supply, too, but it will most likely be less powerfull. In this case, I'm guessing the "fridge" is probably peltier powered, these are pretty linear I believe. So, say the PSU is a bit overrated and the current is more like 5A at 14.4V then that means the "load" is 2.88 ohms, power is 72W. At the nominal battery voltage (12V) P= V²/R or 50W.