If the measurement at the control board was out of spec or showed open (infinite resistance) or short (near zero resistance), check the resistance at the thermistor itself.

Disconnect the thermistor from the wiring harness. You will likely have to cut one or both of the leads, unless there is a connector near the thermistor.

If the thermistor tests okay, the problem is in the wiring harness. You can inspect the accessible parts of the harness for faults. If the fault is not accessible, the wiring harness is foamed in and can't be repaired. Recycle the refrigerator.