99 Jeep Grand...Idle up and down and now a check engine light

Check for loose throttle body or TPS. Or vacuum leak. Cracked or broken vacuum line.

misfires are more from problem injectors, low fuel pressure or injector wiring than from plugs
have a fuel pressure test done to check for problem pressure regulator , problem fuel pump , blocked m/dirty filter
one other area of concern is the EVAP system where the purge valve doesn't vent the tank properly and causes low fuel flow rates

What overheats? The engine or the AC?

Idle air control module is a very probable cause... is your check engine light on? if so stop at your local parts store and have them scan it ( autozone is free). Add surging at idle and stalling in reverse and you named all symptoms of a bad IAC module.

The IAC valve may be hanging high . If you have a scan tool that can display data pids you can see the IAC value . I will check to see the idle specs on it . Which engine do you have .

its most likely a bad sensor. there are Many! have the dealer or autoparts store run a diagnostic.

That sensor is not adjustable. It slides onto the throttle shaft and is screwed in place to the throttle body. Idle speed is controlled by the computer by adjusting air flow through the idle air control valve. If the idle is too high (you did not say) first clean the throttle body bore and plate, then if necessary remove the control valve, cleaning out the passage in the throttle body and carefully cleaning the valve itself, without turning the plunger. If that does not help, you will need to do electrical testing on that and other components to find out what's going on as well as checking all vacuum hoses attached to the engine for cracks or leaks.

my first choice is a throttle position sensor will check my books for the best check proceedure and get back to ya!

Idle prolem could be a dirty throttle body or sticky air idle control motor.
If the Jeep is a 6 cly. the adjustment for the belt is the power steering pump.
If the Jeep is an 8 cyl. the tensioner is on the pass. side of car.

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..