Many signs can indicate a bad thermostat. When this component breaks it either ends up being open or closed. If the thermostat is open, you will have a lot of trouble reaching the normal operating temperature. Especially in cold weather, the engine will run poorly and could even stall. On the other hand, if the thermostat is closed, your car will tend to overheat. This will result in high temperature readings and a blown head gasket. So, it is smart to react whenever the temperatures reach high levels.