Do you mean it just spins and won't start, or that it acts like a dead battery? If the former, as Achipmonk and beltfed said, it sounds like fuel and/ or timing. Not sure which carb you have, if an edelbrock or carter, they can get hot and "boil over" and tend to flood th engine right after you shut it down. Pop the air cleaner off and look down the carb throat when it is real hot right after you shut it down and make sure it is not wet and dripping gas down the carb.
If the latter (acting like a dead battery) then it could be battery, cables, starter, or even may need a heatshield between starter and exhaust. My Suburban used to do the same thing when it got real hot, headers would heat up the starter and when real hot, acted like a dead battery. I added a 2nd 6 ga ground wire from battery to frame (had a spool of 6 ga and ends on the shelf) and made sure everything was clean.
