Classic/Antique Car Repair: trouble starting hot/warm engine, 67 beaumont, heat shield

Question
I have a problem starting my 67 beaumont when it has run for a few minutes.  If I jump the starter it will start but when I turn the key there is nothing there.  I have disconnected the neutral switch and run a new positive wire to the starter.  Any ideas what the problem is.

Answer
It is time to start checking with a voltmeter and find out where the voltage stops when the system is warm. In that era we had a lot of problems with grounds and the starters them selves. There was a factory installed heat shield over the starter that may have been left off at some time in the past.
Brad