Electrical/electronic faults are often temperature sensitive. When an engine is shut off temperatures in some things can increase over running temperatures because it takes time for hot items to cool but cooling systems and air flow has been cut off suddenly. It is not that I think the problem is more likely electrical, it is just the easier thing to eliminate first. The problem could also be in the ignition module. It acts as a pulsing switch to ground on the low side of the coil. The voltage to the plus side is fixed except it is conneted directly to the battery during cranking and then through a ballast resistor after starting. This is done by a switch in the starter.