XJ stall out when it's above 50 F degrees

My daughter has a 97 XJ with 390,000 miles. It's beat up, dents all over , duct tape..but it's all she got right now. And she's kinda attached to the Jeep... It's a 1997 4.0 automatic.
The junker has always run great but lately it's got a problem. When it's about about 50 degrees or warmer outside the thing will start and run ok for about 1/2 hour and then the engine starts to stumble and stalls out. It won't restart for about 20 minutes. Then is starts up and runs ok for about another 1/2 hours.....
When it's colder there's no problem at all.
She lives 200 miles away so I haven't looked at it. I did ask her if she turns the ignition on can she hear the fuel pump go on for a few seconds... She says yes even after it stalls. And she says repeated tries at starting gives off a gas smell.. probably flooding the engine...Wait 20 minutes, go to go for another 1/2 hour...
She took the car to a garage where they checked it and found nothing wrong.
Do understand this Jeep gets very little maintenance....Any ideas?

Probably the 2 most common causes are the ignition coil and crank position sensor. It could be both. Could be just one or the other.

Thanks, She said something about getting an ignition part replaced...Maybe it was the coil and the CPS needs replacement.

Your CPS is heat soaked and causes the computer to shut the engine down. A new one will fix your problem.

In an emergency, a bottle of water poured on the driver's side of the bell housing will cool the sensor down enough that the engine will start.