Scott wrote:
We have a G.E. 2-door refrigerator that's about 15 years old. It's
never had any problems. Recently, I noticed that the contents were
warming up, and the ice began melting. When I turned the main
temperature control wheel to "off" and then "on", the compressor
started up, and it worked fine for a few days. Today, it warmed up
again. I turned it "off" and "on", and it started working.

Any idea on what's going on?

Perhaps the switch contacts on the thermostat dirty and are sometimes not making
contact.