My first attempt went pretty well. Here is the hardware I used, most of what I had available except for the waterproof temp sensor and the food grade heat shrink.
DS18B20 - Waterproof temp sensor - Adafruit
Food-grade heat shrink tubing - Adafruit
Arduino Ethernet Shield (for SD Card)
SHT1x Temp\Humidity Sensor
Tenergy 7.4v 5200mAh LiPo Battery - All-Battery
I started at 8:47pm and the battery lasted until about 6:15am. I didn't get a chance to fully charge the battery but I received a good amount of data. The sketch took a reading and logged it to the SD Card every ten seconds.
What is interesting about the data is the humidity seems to have a direct relationship to the ambient temp of the refrigerator.
Next time, I want to log less often and hopefully get a full data set where the water temp reaches closer\matches ambient. Also I need to track when the door opens either manually or with a sensor (a light sensor would work here).
Overall it was a fun experiment and it is definitely something I want to investigate further and possibly make it a permanent setup - as far as monitoring the refrigerator, if I can get a wireless link. This could be extended further with notifications if the temp rises above a threshold.