Description of the issue and symptoms need to be more clear otherwise folks starting reading into your issue and then down the rabbit hole. I reread your first post. First, you start the truck and it is running. Does it shut off on its own or do you turn it off? Hard starting of a hot engine can be several issues including vapor lock of the fuel lines.

Yes you should start with a know good and fully charge battery. Good fuel with a know good fuel pump. Good starter. If it cranks over easy hot, and it does have spark (continuous when cranking) it most likely is a fuel problem when hot as long as you know it sparks not just on the coil wire, but at a plug wire too.

The overly hot ballast can still we an issue with a coil out of spec to the ballast.