Howdy Texas- glad 2 hear that you got it to spin. If the thermal overload is a round device that has two wires and sits against the dome, perhaps there are clip(s) that hold it in a semi-socket type of prong setup. In the US and US made-for-world market, it would be a round 1 inch diameter X 3/4 inch height device with a terminal(screw) and a wire lead to connect to common. Failure of this is related to repeated high heat operation(caused by high current/motor issues, or just insufficient cooling for compressor and condenser. the fact that it started and ran to cool would indicate that the unit probably ran in a close space or a dirty condition. there are one-siz-fitzall types of overloads that use current as limiter and clip on the terminal box, and generally these will do an adequate job with proper maintenance to fridge. If the overload is klixon type as described above, there should be numbers on the side that can be cross ref'd to newer style numbers. If this is a french product, do you see a brand name for the compressor?
