When we discover the fridge is warm I have tried to move the control thermostat to the coldest position, then off position, then immediately to the coldest position, waiting and do not hear it click on. I have tried also unplugging and plugging back in with no affect. The fridge compressor will click back on usually with in ten minutes after that.

When the fridge is working normally I can move the control thermostat to a colder position and it will immediately click the compressor on.

I have replaced the run capacitor. Thinking maybe the control thermostat is malfunctioning, but want to know what you pros think?

I took the fridge apart and tested the continuity on the thermostat and it appears to be accurate. When off the reading is 1. When on the reading is 0.00. It is possible that I have not performed the test correctly, correct if I'm wrong.