Hi Adam
Sorry to hear that you did not have a clear run - the most common issue for a dead starter motor when hot is exactly as Andy (Forrest Gump) states above, the starter motor is near the header / exhaust manifolds, if you are changing the starter motor, you could go for a smaller (more powerful) unit called a "High Torque" as these generally will have the solenoid a little further away from the heat source, but the most important benefit would be to install an aluminium Heat Shield between the solenoid and the exhaust, do not use a Heat Blanket.
Best of Luck!