Rod,
It is possible that a faulty battery would cause your problem. The coil requires about 8 amps to operate effectively so a flat (or lower output) battery would definately cause your problem (Low primary voltage= low secondary voltage). If the battery is going flat then either it is bad (plates are stuffed or low water) or the generator or regulator is not operating effectively. If you have a voltmeter you should see about 13-14 VDC at about 2000 RPM. If not at this level this could be your drama.
You said you replaced the coil? A standard grey motor coil doesn't require a resistor in series to limit the current to the primary winding and therefore the points: but later model coils MUST have a resistor in series or you will overheat the coil and burn out the points. Most resistor coils have an "R" stamped after the part number - usually found on the base of the coil body.
That said a normal engine runs at about 75-85 Deg C which feels hot with a finger attached to a body that runs at 37-38 Deg C
Keep looking, your getting closer............
Cheers,
Craig