Can I make a refrigerator?

I have a space under the cabinets on my deck that I'd like to turn into a kegerator. The size is 2'x3'x3'. I also have a glycol chiller that is not currently in use.

Could I insulate that space, add an old car radiator and run 25F glycol through it to make a DIY kegerator? I feel like it might go wrong somewhere, but I'm not sure where. Ideally, I'd like to get the temps down to about 32-35F.