I don’t know why or how it’s happening, but it sounds like a thermostat problem. It may just be that those types of little fridges run very cold. Plus you have a lot of moisture in the air where you are. Call a refrigeration repairman, not a refrigerator repairman. Does that make sense? Go to your favorite local restaurant and ask them who they use. Any thermostat can be replaced to run at any temperature you like.
I know a guy in a loft downtown that bought one of those huge, double glass door Coke coolers (like you see in convenience stores) and had a lower thermostat put in it to keep hundreds of bottles of wine at cellar temperature: 55 degrees. I sure do like goin’ to his house. He bought it on the cheap from a store that was closing, and with the modifications it only cost him around $250. (It still says Coke. Looks cool.)
The reason I say not to call your average home refrigerator repairman, is because they charge at least twice as much as a restaurant guy. Should cost you 60 to !00 bucks.