Three common things that can break down when hot then begin working after they cool. Coil, condenser and fuel system. Today's condensers absolutely suck. Sometimes takes two or three times changing it to get one that works right. Your idea of splitting hose to cover the steel fuel lines has worked for some in the past. Making sure you have heat to the intake helps.
When it dies pop the hood and pull the air cleaner. Work the accelerator while looking down the carb. If you see fuel spray then your problem might be in the ignition system. Good luck.
