I hope your temperature gauge is NOT accurate. At those temperatures if it is accurate, you've done some damage or will have if you ran it to long. your guess on the thermostat is probably right. No water getting into your engine to cool it. A quick test is to feel your water hose from your radiator and if it's the thermostat, you'll feel the hose turing warmer as the thermostat opens up to whatever its set at.