It will work.... HOWEVER, it does not have a delay to prevent the compressor from starting during a "normal" off period.... I read in the question section where 1 person fried the compressor by adjusting the thermostat during the run cycle... what happens is, the coolant is circulating then stops, then immediately starts up again hydraulicing the compressor and burns up the motor because it can't rotate.... using extra room in the refer and having filled jugs with water, for thermal mass, will prevent "quick" cycling and help maintain even temps... which is a good thing... One additional safety precaution against quick cycling is.... Have the temperature measuring probe in a container of water... The temp fluctuation of say6-8 ounces of water will be slow, VERY SLOW, and also provide a very stable temperature in your fridge...
I think I read where the controller has a cycle "zone" of 3.5 degrees which is very adequate....
There are controllers out there that have logic and allow for a compressor "lag" setting... I have used Johnson controls and found them to be very good and reliable....
If you are inclined to move into the electronics age, Auber....
http://www.auberins.com/?main_page=index&cPath=1 ... has some amazing stuff on the market and they have an impressive reputation...
FWIW, I've looked at some of the modern electronic controllers and I can't figure out how they work or how to make the work... So, I lean toward the old stuff.... It may be I don't understand their language or acronyms or symbols or who knows what..... I do understand a mechanical dial with numbers on it.... HAHAHAHAHAHAHA......