I'll say it again...perfect application for a PIC/AVR/ETC processor.
However, you might consider restating the problem. IFF the thermostat shuts off the compressor when it gets cold enough, all you need is a latching relay that unlatches the first time the compressor shuts off. Latch the relay with a pushbutton when you load the beer.
Only reason I can think of to care how fast the beer cools is is you're drinking it. Stick an egg timer on the outside to remind you to switch to low.
Or an even simpler solution...buy cold beer...in fact...can you even buy warm beer any more???
Just because you can create a problem to solve, doesn't mean you should... Pass me another beer...please... mike