rough idle with heat on

The heater is just the fan blowing through the heater core so that's a weird problem. Are you using the defroster by chance? Try leaving the heat off and putting a load on the electrical system using everything else...lights, wipers, radio etc. Could be a charging issue but that's just a shot in the dark.

Do you have A/C? When mine is on defrost or the floor defrost my air conditioning compressor cycles every few seconds but it don't drop the rpm that much.

I dont know about the 2000s, but my 97 tj heater system runs of a vacuum system. Theres a small rubber fitting on the intake manifold, you could possibly have a hole in the line, causing it to suck air. Also I would try checking out your IAC. easiest way to check and make sure its working properly is to make sure there are no DTCs, start the jeep, and then while its idling, unplug the IAC. If a code comes up its fine, if no code comes up then you either have a wiring issue or the IAC is faulty. Hope this hleps you out a bit. Good luck

Thanks alot