Why does my 1999 sts run hot when ac is on cools down after ac off?

I assume you are talking about the cars temperature gauge. The reason you are seeing this is because the ac condenser is in front of the cars radiator. So when the ac is operating the air entering the radiator is hotter causing the cars coolant to run hotter. It actually overheats and a/c automatically shuts down. possible causes for the overheating? Can you drive it all day long without the ac? Or does it only overheat with ac on?Check to see that both the ac condenser and the radiator are clean and clear of any foreign matter, maybe you picked up a plastic bag or something like that impeding air flow. Does the fan operate properly? Does the heater blow hot air? If not the thermostat may be the culprit.