We need more info: does it crank at all when hot? Cranking means the starter is engaging, but the engine doesn't catch and run. If it is not cranking then the issue lies with the starter circuit. A starter can become "heat soaked" and not operate until it cools off. If it DOES crank and not start, then the issue may be related either to the fuel pump or the coil. When this happens, remove the air filter and try just a tiny cap full of gas or starter fluid in the throttle body and see if that causes it to run (even if only briefly). If that happens then you likely have a bad fuel pump or a problem with the EVAP system. (You can also confirm this with a fuel pressure test.) If it doesn't run, then you most likely have an issue with the coil. I would look over the coil, cap & rotor, as well as plugs and plug wires. Heat can affect a coil, as well as moisture. At this vehicle's age, it could probably use a good tune up. This wouldn't be a tough problem for a mechanic to find and fix, but it is one of those things you need a hands on inspection of to properly diagnose. I would get this done asap, as it can be dangerous to drive a car that stalls out while moving, as that takes away your power steering and power brakes well.