What happens to the engine temp when you turn the heat on?
Is the air coming out of your vents hot?

 

2X; '91? it is clogged.
If you have a propane torch, a bar of tin and a steel bar out of an old (long) wiper blade it can be serviced.

 

I say compressor clutch cause my lumina did this... overheated... pulled over... shut it off... then it wouldnt start back... the clutch was shot and the starter wasnt strong enough to turn the motor over with the clutch bearings shot... i know his will start back i guess anyway but i was on the interstate running full AC on a 4 hour trip so i probly just burnt mine up faster... Doesnt hurt to pull the belt and at least check the play and see...

 

I have a 94 and I had the exact same issue. I did a flush and then another flush. If you really want to check to see if it is the radiator then pull it and if it weighs more then 15 pounds then it is clogged, TRUST ME. I pulled mine and it seemed heavy but hey I never lifted a XJ radiator before so what do I know. I did the flush thing and still over heated with the AC on, and even sometimes while setting in traffic on the freeway without AC. I went to the junkyard and pulled a radiator and WOW it weighed half the amount!!! they had a scale there and my old rad weighed 24 pounds!!!! the one I just pulled clocked in at 12!!! now in stopped traffic on the freeway with the AC on and no thermostat I sit below the 210 mark!! trust me and just get a new radiator, yours is clogged!

 

I got my radiator on ebay for $10 shipped with 10,000 miles on it... so if you do it check there...

 

looks like the radiator ? i saw alot of gunk inside when i took it out

 

it helps at idle, but you won't over heat with out it. I had a MJ that never had a shroud and never overheated even out wheeling. my XJ had a shroud til I broke a motor mount while wheeling that let the right side of the engine fall into it and break it. that was a few years ago. now since replacing my radiator I've yet to get the red light. and thats including going up to the mountains and through the 120 desert heat out by Palm Springs. a new radiator will cure your problem. I'd recommend replacing the thermostat and flushing the block also. as far as the cooling system getting hot and the radiator cap being cold, that sounds like air in the system. I prefer the Stant cap with the pressure release valve on it, it helps burp the system without getting a facefull of hot coolant. when you fill the system turn the heat on and top it off with the engine running. watch for the thermostat to open. you'll see the level drop in the radiator. keep it topped off. I'll watch this cycle a few times, keeping it topped off and squeezing the hoses to try and release any trapped air. once the engine is warmed up the coolant level will start to rise and if you don't give it a little throttle it will over flow. with the throttle raised to keep a suction in the radiator I top it off and install the cap. after the cap is on let it idle down. let it run for a few minutes then lift the pressure release on the radiator cap.(make sure the overflow hose is connected to the radiator and to the overflow bottle first.) you will see the overflow bottle start to fill up( make sure it's at least to the low mark, so you don't suck air into the system) it will also draw any trapped air with it. close the release valve, let it run a few more minutes and your done. as the system cools it will draw coolant from the overflow bottle. once the system is cold you can double check the coolant level in the radiator top it off if needed, and fill the overflow bottle the the full mark and your done.

 

I had the same issue with my jeep and it was actually my electric fan not turning on, their designed to turn on when ac is in use

 

replace the thermostat and flush out the air in the system.