Thermostat wiring

I'm slowly converting an old Ariston minifridge over to a kegerator . So far I have removed the insulation from the top to check for lines, reinsulated the top with great stuff foam and a piece of wood in there for tower support, flattened the freezer and attached it to the back. Now I am trying to re attach the stock thermostat (I can't afford an external one yet. I foolishly didn't note where the wires attached to before I removed them. I have yellow and I know that's the ground. The other two wires are brown and black. The thermostat has two prongs on it. Does it matter which one I attach each wire to? If so, how do I find out which is which?

I found this site:
http://www.allaboutcircuits.com/vol_5/chpt_2/2.html

so, they appear to be L1 and L2 in a 3-phase line, but I don't really know what that means (and I don't have a grey).

Thoughts?

Should not matter as the wiring to a thermostat is normally just breaking one side of a circuit. However the ones that I have messed with never had a ground wire attached.

Usually you can find a schematic somewhere in or on the fridge, that would clear it up for sure.