If, after checking all the electrical stuff mentioned above consider the following.

Starters get hot. Especially if they are next to a set of headers. They expand and freeze up. when the car cools it works as it should. You can buy a heat insulator blanket or cover from a place like Summit to help this out. Shimming the starter may help as well.

I had a Corvette with dual quads that I later changed to a single quad. The fuel feed to the carb was too much and when hot would vapor lock or hydrolock the engine and I got a lazy turn over and no start. When the car cooled it started just fine. I reduced the fuel pressure from the max recommended 6 psi to 3 psi and the problem went away.