Q: Engine cranks when cold but not warm

A scope (oscilloscope) exam during those few minutes after it starts, and while the engine idles roughly, will reveal the cause. It is either ignition or fuel system related. To schedule a rough running engine diagnostic(https://www.yourmechanic.com/services/car-idle-is-rough-inspection) please feel free to contact YourMechanic and a certified Mechanic will be dispatched to your locale to diagnose and resolve this issue for you. On a preliminary basis, you could try introducing starter fluid, that is enrich the air fuel charge, when the engine starts to idle roughly. If, by chance, the engine smooths out with the enrichment, that would point the diagnostic more toward a fuel supply issue, although you could have a vacuum leak. The difficulty on restarting, as you are describing it, is probably more related to a fault in the starting circuit, possibly including a weak (old) battery. Vapor lock is a condition of fuel in the supply tubing and vapor lock there would not prevent the motor from turning over normally. Hope we can assist you with this issue and if you have additional questions or concerns by all means let us know as well.