I have one of the little blue cube shaped fans, that runs on 2 D batteries. I just position it so it circulates air past the fins, and it does a good job of keeping things more even and cool.
It seems to run for weeks on a pair of batteries, and I only find it necessary in hotter weather.
I think if I were going to add a 12v fan (which sounds like a good idea) I think I'd just run an inline fuse off the 12v supply of the fridge, and put a switch with the fan assembly inside the fridge so you can just turn it on when needed... Unless you really wanted the fan to shut off when the door is open...
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