Is your coil a Bosch? Some VP Engines with Bosch coils have a "hot spark" ignition system. In addition to the purple ignition wire there is a red wire connected directly to 12-volts that supplies voltage when the solenoid is closed--during starting.
Is their voltage at the coil when it wont spark? If so, I'd check the resistance of the primary windings using a multimeter. You'll have to get a service manual or otherwise source the resistance specs for your coil.
The heat issue makes me think resistance. Some "almost bad" wire is carrying just enough juice when cold, but when hot the resistance goes up and there's not enough.