2003 Lincoln Town car. Stopped at a gas station on a cold morning, left car running with heater on, got back in car and dash read running hot. Drove home slowly, car did not want to accelerate properly. Got home and parked it, no smell of antifreeze, etc… associated with a car running hot. Week later changed thermostat, gauge immediately read hot. Weeks later, changed temp sending unit with same results. No possible way car is running hot that fast, drove it around block seemed fine until it beeps telling car is running hot, then it acts like it wants to shut down or not accelerate. What could it be?
Could be a few things going on here. The overheating right after you changed the thermostat is generally caused by an air pocket that has to be bled out of the system. Being low on coolant is a sign of a leak, both internal and external. So if the coolant level was low when this first occurred it is recommended that you check and repair any and all leaks in the cooling system. This can be done with a cooling system pressure tester.(see image)
You can use a infrared temperature gun to confirm the engines coolant temperature. Aim at the hoses before and after the thermostat in order to tell if the thermostat is working. And check to make sure the dash gauge is reading properly.