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This is not a thermistor. This is a well known problem with this refrigerator and the problem is your compressor. The compressor swells up from the heat over time and then it seizes up. The clicking noise is the compressor trying to start up. Eventually it may break free and start working again, but the issue will continue to happen until you replace the compressor I'm sorry to say and that is a $650 repair.
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The defrost thermostat doesn't make a noise to start with, but that would just cause the unit to not defrost if it was faulty. Trust me, I know you don't want to hear that such an expensive part has failed, but I wouldn't tell you it needs to be replaced if I didn't believe it needs to be replaced. This model is very well known for this problem by authorized servicers.