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.
I bought a digital thermometer with min/max from Walmart for $5, but the problem was the temperature would rise quite a bit (above 40F) if the door was left open even for ~10-30 seconds, so it was hard to use the "max" temperature reading.
It would have been more handy if the thermometer's min and max responded more slowly to reject these short fluctuations.
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.