Yes, and what you described sounds just like that or a missing thermostat.
( like someone took it out )
Thermostat is stuck open Thermostat is stuck open
sounds like thermostat is stuck closed, change thermostat
thermostat is more than likely stuck shut from the overheat. Have to be changed.
thermostat is stuck open.
Water Pump or Thermostat. May have to change water pump to replace thermostat.
a bad, or no thermostat might be suspected.
A malfunctioning thermostat can cause your temperature gauge to go up and then allow the gauge to go all the way down. When the thermostat is stuck closed, your engine will overheat and water will not get to your heater core. When the thermostat opens the engine cools down and water flows to the heater core.
Then diagnose it and fix it. There is more than one possible reason why this is happening. Narrowing it down requires diagnosis. Either you have blockage in the coolant lines or passages, a faulty thermostat, a faulty water pump, or a bad belt driving the water pump.
If you're absolutely sure the radiator fan is working properly, have the radiator flow tested. Also, check the thermostat. It may be partially blocked.
There are several reasons why your car may be overheating. Check the thermostat to be sure it isn't stuck. If the car revs up and down, the timing may need to be adjusted.
Make sure it's full of coolant, not just overflow but in the radiator. Check to see if drivebelt is still intact under hood. Thermostat could be stuck closed. Make sure fan under hood is working properly. If temperature fluctuates up and down while driving, then it could be a bad head gasket.
thermostat needs replaced