OK, it took me about two minutes to google that model and find a parts list. It includes:
99271125 Thermal CuttoffThat would appear to be the likely problem. Another possibility would be that nothing is wrong with the cuttoff and instead it's acting to shut it off because it's overheating due to something else, eg insufficient air flow. The actual part might also have identifying numbers that could source it, cross reference it, etc to obtain it at lower cost.
As to the claim that if you bypass it, your fire insurance is voided, I'd like to see some examples where that has happened. Fire insurance typically pays off on your stupid actions. I have yet to see one where they said you shouldn't have used a frayed extension cord to permanently run that refrigerator or you shouldn't have left newspapers stacked around the fireplace, etc, so we aren't going to pay. Note that I'm not saying he should bypass it, I agree, that's probably a bad idea.