Shuts off after engine has warmed up and will not restart until the engine has cooled off?

Hello. Given the age and mileage, I'm betting on a failing fuel pump. It loses pressure as it warms up and eventually can't put out enough to start the car. You can borrow a fuel pressure gauge from the local parts store with a loan-a-tool program.

Here's how to run the test:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

With the key on and engine off, you should get from 40.5-47.0 PSI. The car will not start on less fuel pressure than that. Of course be sure to get it where the car won't start before you check the pressure.

Here's our general guide on changing the fuel pump:
https://www.2carpros.com/articles/how-to-replace-an-electric-fuel-pump

And I'm including AllDatas information on how to remove and reinstall the fuel tank (so you can change the pump) in the attached images.

Let us know how it goes.

Hey Kilo! If the car NOT able to start right now lets do some quick testing to see if we can find a possible path for repair. At the moment we do not know if the problem is mechanical or electrical in nature. The engine NEEDS Air, Spark, and Fuel/Gas to run. I'm going to jump past the air as a problem for now, not very likely to be straving for air. So that leaves Spark or fuel/gas as possible issue. We don't want to throw a lot of money at it to find a path to repairs, so lets short-cut to the chase. Go to the Auto Supply store and purchase a can of BERRYMENS B12 Carburetor Cleaner, Cost about $8.00 or so. Return back to your car and remove the air cleaner hose at the throttle body so we can spray the B12 into the throttle body. But first things first, We need to confirm a Start or No Start for confirmation that it will start or wont start normally by turning the engine over from the key switch. So...using the key switch attempt to start the car. Confirm to yourself if it did or did not start for a baseline of repairs. If it DID NOT start normally we now have a baseline Confirm: No Start. Now you might need somebody to assist the next test. Again using the key switch spin the engine over and spray B12 into the throttle body, just a small tap of the button on the can of B12 is all it takes, DON'T get crazy and empty the can in there, just a quick spray while the engine is spinning. What happen??? Did it try to run or actually start for a few seconds or did this have no effect at all on the engine? If it tried to run or putter then you have confirmed spark to the plugs and there for the issue would be a fuel delivery problem. That gives you a starting point for possible repairs now. A fuel issue, might be electrical, might be mechanical. If this test had NO EFFECT on the engines ability to start then you have revealed a ignition problem. NO SPARK = NO START. You MUST have spark first!!! So for the cost of the B12 you just found a possible repair path to follow and you now know where to start your repairs. There can be other issues beside spark, but you need to start with spark and work your way outwards. Good luck!

Well put Cut213, also this video may help as w ell

https://www.youtube.com/watch?v=lXLJbuAZ4CE

Please let me know what happens.