Now if you're feeling really daring, you could cool it using Boyle's Law by running chlorine vapor through there from a tank of pressurized liquid chlorine which is fed with a pump from the vapor that just ran through. It should look like this:
_______________________ _________
_________| |_____| |______
| ______ Small pipes around beer ______ Pump ____ |
_____________| | |_______________________| |________| | |
/ | | |+++Heat Sink
| | | |+++Heat Sink
| Liquid Chlorine |_______________________________________________| |+++Heat Sink
|__________________________________________________________________|
The chlorine cools as it expands up from the pool of liquid chlorine. The pump has pressurized the chlorine in order to move it through the small pipes around the beer, where it absorbs heat and is then pressurized back into the tank of liquid chlorine. This requires fine tuning in order to avoid liquid chlorine moving around the system (which defeats the purpose) or hot gas going to cold beer. Remember to put a heat sink on the pipe coming from the pump into the tank in order to help the gas to condense more quickly. The only danger to this system is the toxic and explosive nature of the refrigerant. So don't smoke around it or tune it while inebriated. If all goes according to plan, then it should work beautifully. Now since I've never built a refrigerator or worked with chlorine, take my advice with a grain of salt and correct me if I'm wrong.
-Penguin