If it overheats while it is moving it could be a couple of things. It could be a bad thermostat. Or it could be a blocked radiator.
The cooling fan isn't supposed to come on until about 220F. They will remain on until the engine cools to about 215F to 210F. If while the car is sitting stationary and the engine gets above 220F and the fans don't start it could be a couple of things. Look for a blown fuse in the fan circuit. Look for a bad temperature sensor. I believe there is a relay located in the fan circuit. This relay could be failed. The fan itself could have failed.
Also, when the water pump was replaced was the air bled from the engine. There is a coolant transfer pipe which comes out from the top of the water pump and travels along the front valve cover. In top of this pipe there is a small bleeder screw. This is to remove air from the top of the engine when servicing the cooling system.
I also had this happen to me once. It is most likely a rare occurrence but strange things can happen. Once I replaced a water pump and found the engine was still over heating. I looked at everything possible except the new water pump. I had replaced it so this should have eliminated the water pump. As it turned out, the new water pump was faulty. There was a bad weld connecting the impeller to the shaft. This allowed the impeller to slip on the shaft and the engine would over heat. So just because you replaced a part it doesn't always mean that the new part is good.
If the overheating happens very quickly it could be a more serious problem like a blown head gasket or cracked cylinder head. With a blown head gasket or cracked head the engine overheats ridiculously fast. Within a minute or two after it is started. A pressure check of the cooling system will help identify this problem.