1992 toyota celica convertable fails to start after hot

Had the same problem. It is in the distributor. Mine would fail to start and if I waited 1hr it then started and ran fine. Mech told me something in the dist got hot and had to cool off

clogged catalytic converter

Could be the fuelpump but did you check the compression when the vehicle is hot? Could be wrong setting on valves.

Fuel filter yes, could be the crankshaft sensor.

If it felt like running out of gas it probably was, Check fuel delivery first your fuel pump possibly died.

When it's not starting, you need to perform the basic troubleshooting steps to narrow down the possibilities. Check fuel pressure, check for sparks, etc. See tips at the link below.
Do It Yourself Diagnosis and Repair

The steering lock may be binding the ignition lock cyl preventing the key from turning or the key may be worn out. Try turning the steering wheel back and forth while wiggling and turning the ignition key. To get the alarm to turn off without starting the car try locking and unlocking the vehicle from the passenger side door. There is a micro switch on the drivers side door lock cyl that may be bad and preventing the alarm from dis arming. This is all providing it is a toyota factory alarm sys.

timeing belt if it turns over and nothing or timeing is off

check the map

Sounds like a vapor lock. If it's possible, try re-routing the fuel line to the injectors. That should help