Wasted power, possibly burn up the compressor..
Freezers tend to have MORE insulation than a dorm fridge so converting a dorm fridge into a freezer while technically possible by replacing the T stat can be done, it will use much more energy by having to run the compressor longer and more often.
It is for the insulation reason as to why some folks have converted chest freezers into off grid refrigerators. The high insulation R value and the chest configuration means the compressor will run very little and that makes it off grid compatible.
You are better off to buy a small chest freezer, yes, they are a bit more expensive than a dorm fridge but they ARE purposely designed for the job.
Use the right tool for the job..