do a diagnostic...see if you get a coolant temperature sensor code
sounds like the sensor unit for the gauge in your car is going faulty
i suspect even with the thermostat stuck open (or completely taken out), the car should reach a reasonable operating temperature sometimes, but may not maintain it when driving.
you can check the thermostat just to make sure its operating as it should
also, what kind of outside temp is it where you live---climate wise??