Chris,
I have cooled Gilas in a refrigerator in the past—no problem. However, you don't want to use the refrigerator’s thermostat (it’s set point is too cold). I would recommend that you build a controller from something like a Ranco or Johnson Controls digital thermostat. Wire it so you can just plug the power cord of the refrigerator right into the thermostat. These controllers are very accurate and you also have control over setting your dead band with them. Since the set point of the external controller will be higher than that of the refrigerator thermostat, the external controller will do all the temp control (the contacts in the refrigerators thermostat will always be closed since your control set point is greater than the refrigerator’s thermostat set point—does that make sense?)
“I know they tend to dehydrate things”. That’s not exactly true. It is true that cold air can hold less moisture than warm air. There is nothing about a refrigerator that dehydrates things other than the cooler air inside not being able to hold as much hair as warmer hair. At the same time evaporative water loss will be less at lower temperatures. If anything, being a closed space, you could control the humidity better in the refrigerator than you could cooling an entire room, for example.
As far as air exchange, depending on how many animals you have and the volume of the refrigerator, you will probably be fine just opening the door every week. Alternately, you could use a small aquarium pump to slowly pump fresh air into the refrigerator. You would use aquarium air tubing to pump it in and another piece of tubing to exhaust the air (for example, pump the fresh air into the bottom of the refrigerator and exhaust it at the top).
If you need more detail or have any specific questions, just ask.
Best,
Mark
www.DrSeward.com