1968 Firebird won't turnover after a trip, but will if left for an hour or so

Thanks, I thought that is the problem and actually still do. The solution is still failing me. I put in the heat shield, but it didn't stop the problem. Cable is new. I guess maybe I'll try a new starter. Thanks again for your help!!

not sure if this could be the problem but I know with older cars like my brothers 65 Mustang back in the day the problem with that car was the ignition solenoid or what is now called an ignition coil pack It's like a little round cylinder thing and is flash light sized thats connected to the distributor and it took power from the starter "I think" and transported it into the distributor via the distributor cap I remember that was a problem it was part of the ignition circuit and if it failed or got too hot the car wouldn't start so It could be your solenoid it's like usually on the firewall or something with those cars as I remember back in those days hope that helps I don't know just trying to throw some possibilities out there but it probably is the starter?

I have a 78 Sunbird Safari and when this happened to me, it was just a $16 starter solenoid.

I have a '68 Firebird and it is doing the same thing !!! If you figure it out please let me know and I'll do the same. Bobby P