Certainly sounds like heat soak on the starter. Engine heat will spike shortly after you turn it off, then begin to cool. There's a period of time where that heat soaks into the starter before ambient temperatures start to cool and take heat away from the starter and engine. That may explain why after a short period you have trouble, but after a longer period of cooling, things start to work again.
Health of the battery, starter solenoid and the windings in the starter, or corroded/undersized starter wires may all contribute here.
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-Jason
1969 Pontiac Firebird
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