I'm not an engineer but my understanding is that the purpose of a thermostat is not to keep the engine cool but to let it warm up quickly and keep it at a more efficient operating temp. A stuck open thermostat most often leads to a complaint of a heater blowing cold air. I've never heard of a stuck open thermostat leading to overheating.

Save a life, adopt a senior shelter pet.
The three main causes of blindness: Cataracts, Politics, Religion.
Name your dog Naked so you can walk Naked in the park.