Kristen,
Don't let Warren drive Pepe. The stopping after it gets hot sounds more electronic than carburetion. Do you have the MSD 6-AL ignition in it? You could have a module or even a wire that after all this time is close enough to some heat source that it is going bad until it cools off. I would give you a long technical explanation of how to check for this but I don 't know how.
Ron
