2005 Kia Rio

I have a 2005 KIA Rio with 72,000 miles on it. Not all the time but sometimes the temp gauge will go into the hot then come back down to the temp it normal is just at half. This only happens when you drive it. You can let it run all day sitting still and its fine. After parking it and shutting it off the coolant comes out the overflow bucket. The coolant is up in the neck of the overflow bucket. I have replaced the thermostat with one from the dealership. Replaced radiator cap , also had a pressure check done. Everything was fine. The timing belt broke at 72,000 so I have redone the head and all gaskets was replaced then. The belt makes a noise off and on that runs around the water pump. Not sure if that has anything to do with it . We are really confused as to what it could be . I’m hoping you will have some insight .