Could be the battery, could be the starter, could be battery cable connections. It takes more amps to turn over a hot engine. Heat soak on the starter is common but I have a stock starter, no heat shield and headers, never had a problem. If the starter is going then yes, heat soak could cause the problem.
A weak battery is another possibility. Like I said, it takes more amps to start an engine that is hot and just shut down a few minutes before. Do you have a known good battery you swap into it?
If any the battery connections, ground cable connection to block or positive cable to starter are corroded they should be cleaned up.
I would start with the basics before replacing the starter. Go to an auto parts store, they can test the battery and the amp draw of the starter. That should tell you if it's the battery or the starter.
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Hank
70 Chevelle SS396(454), M20, 3.73
My Chevelle
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