Hi, I've got a '95 cherokee that had the same "hot" problem. This was unfortunately discovered on a 600mi trip to branson in the middle of summer. On the way there I stopped in one town and got a new radiator cap to see if radiator pressure was the problem. It seemed to help a little and we mde it there ok. On the way back, however, the temp outside was around 100 deg. and the Jeep just wasn't liking that at all with the ac on. Had to run with no ac and windows down on the return,even had to run the heater on high just to run 60 mph. "HOT"! Back at home I tried much of the same as you,but discovered the radiator, although looking passable, was severely rotted out. $100 later all was well again and the ac even worked in traffic. Money well spent as even for the occasional maint. expense, my wife and I both agree, this cherokee with over 160k miles has been the best vehicle we've owned.
As for the high idle,try the IAC or "idle air control" valve. Sometimes taking it off and cleaning it with carb cleaner will fix the problem if it's gummed up. Just unplugging the conector should also tell you if it could be suspect. When unplugged the idle should change quite a bit.
My husband is trying to figure out how to fix my 1989 jeep cherokee. It was running hot, and he has replaced everything but the radiator. It still runs hot and it idles very high and he can not figure out how to get it to stop. He has checked every hose and electrical plug and nothing makes it change. Does anyone have any idea of what he can do to fix this besides shoot my jeep?