Bob,
if the battery cables/leads/terminals are getting hot that means either there is a poor ground some where, weak battery, bad starter, bad cables. Make sure that the replacement starter is the one recommended for the car. I know that there are serveral listings for starters for that year on GM cars. Make sure that the one you have is the correct one. My battery has 950 cranking amps. It does take a lot of amps to start these cars after they get hot. What I would do is get the car from the mech, take it for a 30-40 minute drive, come back and see if you can duplicate the problem. Hopefully it will repeat the problem and allow you to get it corrected.
Good luck and hang in there.
H.D.