hot engine wont start

A friends 88 sable keeps breaking down. She has replaced bttry, starter, & alternator. I thought it was ground wire, but problem still persists. I borrowed car for weekend to diagnose and after engine heats to normal temp if you shut it off the car wont start. it acts like a dead battery. its holding a charge and alt is putting out 13.48 volts when running. Anybody got any clues? Oh, I just now found out that she has gone thru numerous starters the past couple of years. Now what would cause that?

first of all if she is going through starters she is probably starting it hard... starters actually only have a couple of hours of true life.... if i remember correctly its only like two hours of run time.... or something like that. because you only run it for milliseconds at a time when you start the car. anyway. if the car is overheating i would first check the coolant level she may be low on coolant. also check the radiator, radiator hose and resevoir cap. if there is air in the line it will make all sorts of things go wrong. my 93 is starting to have problems with the radiator, and the temp gauge.. it will not read properly if there is air in the line... it may also make the temp gauge sky rocket when the actually temp is not that high also causing the heater in the car not to blow hot air... but may do so in spurts switching between hot and cold depending on the whether... i noticed this on a cold day recently. start with that and let me know whats new