I've got another suggestion that would explain the chronic undercharge condition of the battery, and the hot wire. Take the wires off the back of the ammeter one at a time, and throughly clean the contact area. (Disconnect the battery ground cable first.) If there's a loose or dirty connection at the ammeter, it will generate heat, and also fool the regulator into cutting back the generator output, resulting in an undercharged battery. Try measuring the voltage output at the generator Armature terminal with the engine at a fast idle 1,500 RPM or so, and again at the battery positive post. The two readings should be within 2/10 volt of each other. If there's more voltage drop than that, you've got dirty points at the regulator cutout relay, or a loose or dirty connection at the back of the ammeter. Either one will result in a chronically undercharged battery.
Jerry