Hydra1/2ton,
Welcome to the Stovebolt. On a rig of your vintage that has been converted to 12 volts, there are two options for supplying reduced running voltage to the coil. One option would be to install a 12 volt, internally resisted coil. If this option was used, I don't know why repeated starting attempts would heat it.
Option two would involve a bypass circuit somewhere that supplied full battery voltage during STARTS, but reduced voltage when running. This combination 'might' result in a warm coil if you attempted to start it a whole bunch of times.
The most typical scenario would be running into the house to catch the second half of the Lakers game and leaving the ignition switch ON! The key switch is different than most folks are used to, so this can happen, and this will undoubtedly heat the coil.
Stuart