Mass power supply for the starter. There might be a thick cable running from your battery to your starter motor. Might be loose or corroded or missing.

Explanation:

The starter motor gets it's power via the alternator (+) and via a own cable from the battery or the bodyshell (-). When this cable is missing, the starter has to get its (-) via the engine itself. When this gets warm, its resistance is rising. When the engine is hot, the resistance is so high that there's not enough power for the starter.