Everything was going so good

Do you have electronic or point ignition?

What we know...

  1. The car starts easily when cold
  2. The car is hard to start or no start when it is hot.
  3. Car did not shut off with key in off position.
1 and 2
Sometimes engine heat makes restarting difficult, fuel delivery issue.

3 not shutting off,
I would do as mentioned earlier,
Check the under dash wiring from the ignition switch thru the bulkhead connector to the ballast then to the coil.

check for battery plus voltage with key in run and start WHILE it is in a no start condition