When I start the car in the morning and the engine is cold the motor accelerates up and down.

At the same time after the engine worms in the morning and I drive it, the water thermometer goes from normal to high then back down. It does it a few times for about 30 min. Lastly, when I put the heater on hot air, out of no ware it get cold for a few minutes and then back to normal(hot).