Thanks for the links. I have no idea about the compressor (as far as I've seen not even the terminals are marked), but the OC is a Klixon M(or maybe N)RA 2969 and looks just as you described. maybe 1" in dia., a screw and a wire to the compressor.
Only problem: it sits flush in the dome. Gonna have a look at it soon. Spent the last 2 days at a flea market (local scouts sold lots of old stuff, real fun to dig around), so I didn't have much time to spend on the fridge.
IIRC it operated for several (close to 10) years built into the kitchen cabinets, then it sat in a corner of the kitchen butting up against 2 walls. When I ran it w/o the OC it sat in the middle of the workshop with lots of air around.