Once the coolant reaches the thermostat temp rating it stays open. It might partially close if temp drops appreciably. Just a guess, but I know it stays open at or above temp rating.
Watching my temp on multiple vehicles, the needle moves--more dramatically on some vehicles than on other vehicles. Usually, this is caused by the opening and closing of the thermostat. Discussing this with a mechanic, the thermostat does open and close to allow the coolant from the radiator to be regulated. Unfortunately, the regulation occurs after potentially cold coolant has already been drawn into a hot engine. The thermostat does not know if the engine is running or not--only the coolant temp.
When the temps were -20 or so, we used to put cardboard in front of the grille, so we would have heat. The engine temp was usually OK.
