As William stated, I would guess it's cranking fine hot or cold, but would like a better description.
This likely isn't your issue since you stated it starts fine cold, but one thing I often see missing on a points ignition car is the hot wire that runs from the "R" terminal on the solenoid up to the coil. This provides a full 12 volts while the ignition is in the crank position. Otherwise the points are dead while cranking and only light off once the crank position is released. Sometimes makes starting a car that is still running points hit or miss, and most times requires more cranking than should be necessary to get the engine to fire.
Since it's a hot start problem, taking the starters ability to crank while hot out of the equation, most often it's the quality of the pump gas being used. The ethanol fuel today is more susceptible to heat soak, especially if you're trying to run a lower octane. Any part of the fuel system close to heat is at risk. Some of it can be cured or subdued to some degree with various things you can do, but in some cases it may just be the nature of the beast.
