Engine cuts off when hot and will not start back until it cools.

Sounds like a "HOT SOAK" problem.
Starter gets hot,it lacks power to crank the engine.

Possible "Vapor lock".

Check for engine codes.Possible bad temp sensor for ECU.

If fuel delivery is suspect ,try starting fluid into intake when "no start" occurs to diagnose fuel problem.

check coolant temperature sensor

Has anyone checked fuel pressure cold and hot ? Check engine light on ?

Hi there have you tried the ignition coil as this sounds like the coil is getting hot and creating an open circuit thus no hi tension voltage to the spark plugs,once it has cooled done the car will start again until
it repeatedly gets hot and shuts down very common in pre coil pack vehicles,easy test try a spare coil and drive for same or more distant if not fault them coil is U/S

Check your ignition coils or ur fuel pump

After you kill it, when you try to start it back up, does the starter turn the motor? Or is it froze up (will not turn over)?

Hi.. I had a very similar problem recoverrd to are workshop by the A.A around a month ago.
Exactly the same problem (left to cool started.? Once worm or hot engine just turning over ?)
Afdter reading all known folts and finding nothing to do with what I'd wanted. It took some time ?
Cutting it sort if found when I replaced a intermittent faulty fuel relay and run till engine hot (untill cooling fan cut in) Then turned off engine .. on turning key to see if this had cured my problem?
The engine started frist turn of key after repeating this a number of times .. this car was now starting fine (whether hot or cold)
Problem fixed..
Hopefully this will be of some help to yourselves
Hears hopping
Don Milward Premier Garages

You need to replace your crankshaft position sensor located by the harmonic balacer. These sensors heat up and cut off the engine until the sensor cools down. This happens with age and it is not specific to GM.

Replace the TFI module. Ford back in 1986 thur 1993 had problems like the one you wrote about. TFI module gets hot and shuts car or truck off then when it cools sometmies starts and sometimes not.

you say the engine shuts down when it gets hot if it runs rough before doing so it could be the coolant temperature sensor allowing the engine to  overfuel  if the engine cuts out in a couple of seconds but sounds smooth it could be the fuel pump , if it cuts out instantly its electrical.