2002 jeep gr. cherokee laredo overheats only when sitting at an idle, temp comes back down when heater and fan are turned on full blast as long as jeep is moving

By the blower motor ,there's a resister,replace.

Fan relay or a temp sensor

Electric fan not turning on or a bad fan relay switch.

Bad themostat, dirty radiator (the front of it), corroded interior core of the radiator, weakening water pump, bad radiator fan.....just to name a few. More than likely? Low antifreeze level, or the thermostat.

run scanner

It sounds like it may be your electric cooling fan. When the car is sitting idling does the fan behind the radiator ever come on? If not then this is your problem. Your car doesn't overheat when it moving because you're passing air through the radiator with the movement of the car. The problem could be the fan itself, the fan relay, or a temperature sensor.

Many cars have a thermoswitch threaded into the radiator that activates the fans when engine exceedes normal optimum opperating temp. This sensor may have failed , or one of the 2 wires that go to it may have come unpluged or broken

Thought I answered this one already. but here's the short version. Yes , change the t stat after servicing wp. They become unreliable after any high temps (above normal). Check the electric fan, and the mechanical fan to make sure both are working properly. If all else fails. remove radiator and back flush. often overheat or high temps can loosen block rust and obstruct part of the radiator core.
When re-filling, turn heater on high to eliminate air pockets in system.
Good luck with it
If you need more info, just ask!

You can test the system by disconnecting the engine temp sensor that turns on the fan, the engine computer will go into failure mode and turn on the cooling fan, if the fan does not run check for voltage at the fan with a 12 volt test lite..

the only problem that vehicle has is with cooling fans is relay/module or electrical harness to module that burns up located behind and under right front headlamp assy must remove headlamp to access relay/module that is what powers up fan motor module assy.