In normal operation, the pistons are much hotter than the cylinder walls.
When you shut off the engine, the heat will transfer from the pistons (making them smaller) into the cylinder walls (making them bigger) This would result in MORE clearance, not less.
The idea that an engine (as opposed to a starter motor) will heat soak and get HARDER to crank is nonsense. Even the oil is thinner, resulting in less load on the starter.
The problem is in the starter, the battery, the cables/connections, or some combination of starter, battery, and cables. If it cranks good when cold, you can "probably" rule out the cables 'n' connections.
First guess: Hot starter windings increases the resistance making the starter less powerful.
Second guess: The battery is too small, or worn out.
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