Tempature problem

1996 lexus ls-400 new water pump, themostat car runs hot when stopped for a period of time then when it moves tempature gauge returns to normal

That is a symptom of a radiator fan not functioning. You likely have two radiator fans.  One comes on when you turn on the A/C, the other comes on when the engine gets hot enough. 

Does it overheat when you have the A/C on?  Next time it starts getting hot try stopping with the A/C off and the engine running, opening the hood and see if either fan is running.  Then try turning on the A/C and see if one fan turns on and see if the temperature aactually goes down some.

If the fan is not running it may be the fan, the temperature sensor (it may be a different sensor than the one the gauge uses) or wiring/fuse.