Yes, the halogen bulbs (being higher wattage) will draw more current through what is already too small guage wire. The alternator with greater charging output will keep the battery charged with the greater draw from the halogen headlights, but it won't protect the wiring from overheating. The fix is to run larger guage wire to the headlights. You can use the existing wire to control relays and the relays will actually turn on the headlights. Go to
www.danielsternlighting.com/tech/relays/relays.html for instructions on how to upgrade your headlight circuit. You should be able to do this in about 2-3 hours.
BUT BACK TO THE ALTERNATOR/generator question. You will still be alright with a generator, even with halogens, if you don't drive a lot with your headlights on. While I don't have halogens, I do have two fog lights. Occasionally, I drive with both the fog and headlights on and the generator still charges the battery.
FWIW, I would install the halogen headlights with the P700's first with the relay system, before I consider the switch to neg ground & installing an alternator. If you don't experience charging problems (the little red light in the tach will tell you), I would leave the car as original with the generator and pos. ground.
Why do the wires get to hot? Well, again to0 light a guage wire, but generally bad connections (the bullett connectors get dirty and corroded), usually the ground connections. Whether you go to halogens or not (regular bulbs are available too), or add relays or not, it would be a good idea to check, clean, replace if necessary, the bullet connectors.