If you purely want to guess and throw parts at it, chances are the PIP is acting up. To get a fresh one installed involves pressing off the gear on the bottom of the distributor. Most folks simply get a reman'd distributor from the local parts store for 100 bucks or so.
The other likely (though less likely) candidate is a bad TFI module. Parts stores can test yours.
From there the list of possibilities gets more sparce.
Sometimes you can narrow down which it is by checking for spark and injector pulsing when it won't start. It's always a good idea to retrieve self diagnostic codes as well. You need only a paper clip to do so.
The PIP isn't easy to replace, unless you have all the right tools (including a press). It's easier to buy a remanufactured distributor from your local parts store and try it out.
Do you do your own maintenance on your 'Stang? If you haven't before, but you want to learn, this is the place (and time) to learn.
I had a similar problem, but it was a cheaper fix. The distributor cap and rotor (inside) eventually get corroded and wear out. A worn cap & rotor can also cause this same problem. You can remove the cap without pulling off the spark plug wires and check underneath for corrosion.
Either the distributor or the TFI (the gray/silver component with fins, it's under the intake hose) are getting heat-soaked and aren't working right anymore. Since the problem only happens when the car is hot, it's hard to diagnose. I would recommend trying a new distributor first, then drive the 'Stang around for a while. If it fixes the problem, you're set.
If the problem still happens, the TFI module is next. You'll need a "Ford Ignition tool" or something similar to remove the module off the heat sink.
If it was a Fox my first guess would be the TFI but theyre slightly less prone to fail after they were moved away from the engine. Like has been said, the pickup inside the distributor is a likely culprit. It controls fuel delivery and spark and your symptoms sounds pretty accurate to one thats on its way out. TFI module is the cheaper of the two but that can be easily tested at most parts stores. If it was me, Id have the TFI tested to rule that out. If it is, 50 dollars or so will get you a new one from the aftermarket. If that tests good, theres a pretty good chance its the profile ignition pickup aka the stator signal. You could always do like the wannabe mechanics due to me at the Advance I work at nights. Buy the distributor, try it out. If it works, keep it. If it does the same thing, bring it back and say you ordered the wrong part. Happens all the time when Im on. Its obvious whos going to do it too, because they dont even know what half the parts are called, let alone how to properly diagnose them. Good luck to you in any case.