How to diagnose thermistor problem
In my experience, the thermistor is a good place to start. Replace it and see if that works. That’s the simple solution.
If you want to further test the thermistor, use a multimeter to to measure the resistance while wiggling the thermistor to test for breaks in the wires.
If you have the spec sheet on the thermistor, you can measure the resistance of the thermistor and see if it matches the spec sheet. Use ice water as a reference if necessary.
Just replacing it is probably the simplest though. You should keep extra thermistors on hand anyway for when it does go out.