DeadCellM60

I have a 96 XJ, 4.0, bone stock, and on occasion while driving it will simply shut off, almost as if it ran out of gas.

It goes further than that though: It only has ever done it in extreme heat conditions where I have been driving longer than an hour and a half in 90 degree weather or so where it reaches the point (I suspect at least) that all the coolant has circulated throughout the system. While driving at any appreciable speed, say 20, 25 mph+, she runs right at 210 where she always does. But when I hit heavy traffic or any stop-and-go environment, it begins to idle low and the engine will eventually cut out and die.

If I try to start it right away it will crank until the battery dies but will never turn over. (I have spark as well as fuel each time I have checked). However if I let her sit and cool off for half an hour she will start no problem and will run until the process and circumstances are repeated.

I initially suspected it to be the MAP Sensor where maybe the heat was screwing with it and causing it to tell the computer there was no air coming into the system (no air, no combustion), after all, it is right on top if the intake. Before I made any moves though I thought I'd see what you all had to say. Maybe I'm missing something obvious?

DeadCellM60

It seems to me the issue has got to be electrical somehow because of the stringent conditions under which it happens. Anything mechanical would happen much sooner and more consistently right? I am at a total loss. Any help would be greatly appreciated before I start throwing parts at the thing.

*And a detail I missed in the initial post:
When in traffic and before it begins to idle low, the Jeep will reach temps upward of 240 (just at the tick mark before it gets in the red). That's when it has died most often. So extreme heat is always the culprit it seems.