sorry to hear of your misfortune :(
the heat tells you that you have high resistance between the battery and the starter.
if you have done so already clean the positive post and cable and put a little grease on it when you go back together.
also check the connection at the starter, same principle, clean and tight.
beyond that your starter is failing (drawing too much current)
does that make sense?
just got called to dinner, i'll check back with you in 30 minutes, if you have further questions.