Cool starter project! You could solve this problem in a couple of different ways.
The most obvious would be running the circuit off of the fridge power supply directly. I'm not sure how comfortable you would be with re-wiring your fridge though. The potential to start a fire is probably relatively small, but it still exists.
Another option would be running a small heater around the battery itself. It shouldn't take very much power to keep a 9v warm enough for minimal losses in a fridge. (http://www.bipowerusa.com/products/bipower-bl9v-u.pdf)
I've pondered having the device use the fridge bulb plug for power. But that's only designed to be powered when the door is open. So we can use batteries or capacitors, which is back to problem #1. Or we can tape the door switch to be always-on, but I'm concerned about the power drain.
Ultimately, this device would influence refrigerator manufacturers to include this technology in their base models. I'm tired of fiddling with dials to try and figure out if my fridge is at 2C or 5C or -1C. (38F or 42F or 30F). I want fridges to know what their internal temperature is, and what we think it should be.
I'm thinking more about ensuring wide adoption through low-cost and low-intrusiveness. Modifying my fridge would make a good Hackaday post, but not such a good Kickstarter project.
(Maybe even a fridge/freezer with a barcode scanner and multiple compartments -- give it a database table of appropriate temperature ranges for different foods and let it set the temp in each compartment automatically. It could keep your ice cream from melting and prevent your lettuce from freezing? How about sectional temperature controls, like in car cabins?)
True, but if someone is going for low cost off the shelf 9 volt batteries it could be a temporary solution. Plus they would learn how to build an electrical heater, which is a useful skill to have for lots of applications.
The most obvious would be running the circuit off of the fridge power supply directly. I'm not sure how comfortable you would be with re-wiring your fridge though. The potential to start a fire is probably relatively small, but it still exists.
Another option would be running a small heater around the battery itself. It shouldn't take very much power to keep a 9v warm enough for minimal losses in a fridge. (http://www.bipowerusa.com/products/bipower-bl9v-u.pdf)