1989 Ford Festiva Perplexing problem

This is a real quandary, and I need help please! The car runs great until you cut it off. After it sits for a few minutes, when you start it and try to drive it again, within 200 yards, it will start to buck and jump and jerk like a bucking bronco at a rodeo. Horrible. Then when you cut it off and try to drive it again, it will simply konk out before even moving two feet. Then it's no good at all. BUT, if you let it sit for five hours and cool Completely down, it was start up and run great again. I stupidly got a new carb, but the people at the carb shop said it is definitely not a carb problem, that it has to be electrical. Since this is an 89 Festva, it is pretty simple and old school. We have already changed out plugs, wires, distributor cap, distributor rotor, fuel filter, thermostat, oil, filter and more. The mechanic I had (number 5) went through his 17 point checklist and said every thing checked out. I run pizzas, so I am really really stuck without a car, now without a job, and soon without a place to stay. Please help! Thank You in advance.