Hold off on that computer. Replacing the computer should be a "diagnosis of exclusion", meaning that everything else has been ruled out before you condemn the computer. Yes, the computer can of course fail, but generally speaking they are pretty hardy in comparison to other electrical components on the 4.0 engine.
If it starts good when cold and you only have symptoms when warm, you are experiencing a
"thermal" (heat related) failure.
It is very important that you test for spark when the engine won't start. Testing has to be done when symptomatic, as these components may test as good when the engine is cold and starts. Has that been done? Pull a plug, keep it attached to the plug wire, place the plug electrode near a good engine ground, have a buddy crank the engine while you watch. Knowing whether you have NO spark or WEAK spark when the engine won't start is absolutely job #1.
If you have no spark, the #1 suspect is the crankshaft position sensor. Without the input from that sensor, you will have NO spark and you will have NO fuel going to the fuel injectors. I've included a link a thread on the crank sensor below. The crank sensor is probably the #1 sensor failure on the Jeep 4.0 engine.
The #2 suspect for thermal failure / loss of spark is your ignition coil. It can be tested with a meter and a manual. You test for both primary and secondary resistances.
Although more rare, it is possible for the camshaft position sensor (located inside the distributor) to fail thermally as well. That too can be tested.
Don't throw parts at this on a hunch. Terribly ineffective and gets expensive in a hurry.
Test your way to a solution! Good luck and let us know what you find!
Link to crank sensor information:
http://www.naxja.org/forum/showthread.php?t=1044073