You could do this today without any sort of "smart" appliance for about $1.00, $50 if you are being lazy. Just get a super simple micro-controller and radio on a board and throw it into your fridge. Have it record the temperature at a regular interval into a ring buffer and poll it periodically from a chron script. Get your power from the light switch in the fridge door. Alternatively, a Li-po or Li-ion battery can last an extremely lond time powering a little micro in a refrigerator. If you put a $0.02 photo diode on it, you could also track how often the door is open.

If you went the full on $50 route and bought a pre-integrated board with wifi and a full linux stack, you could even have a push notification to twitter or email or whatever when the temperature goes out of spec.