You are giving advice on and making comments on things you evidentely do not fully understand. That sort of thing may be ok on the DIY sites you are on, but that sort of thing is not acceptable on a site where there are so many professionals in the HVAC industry who have to correct your misinformation.
When a furnace overheats, several things happen, depending on the model of the furnace. At the very least, more than just shutting off the gas valve occurs.
It doesn't matter what type of thermostat is installed on any furnace dependent on the thermostat to initiate furnace operation. All any such thermostat is is an on/off switch that is thermally controlled.