First time posting so pls be kind.
2011 GE GTH21KBXAWW keeps running. This is a simple mechanical unit. No computer.

I found my lettuce was a bit frozen last week when I pulled it from the refridgerator. I believed the thermostat had failed because the refridgerator did not turn off. The compressor continued to run and it continued to cool.

I could turn the thermostat to the OFF position and the compressor would stop. Then I would turn the thermostat up to 2 (with 7 being the coldest). The compressor would not immediately turn back on. However, once the compressor came on, it would continue to run.

I replaced the thermostat with a GE brand from a dealer. It's doing the same thing. Could this new thermostat be bad?

btw: I tested the original thermostat by checking for continuity with the sensor a bucket of ice water. There was no continuity between the contacts. I pulled the sensor out of the ice and got continuity between the contacts. Put the sensor back in the ice and the contacts in the thermostat did not open back up.