An immedieate fix to the symptomn of an ice dam is to make channels for the water to flow. I agree w/ Jay, don't hack! You might try taking sone old nylon stockings, filling them w/ coarse rock salt, and placing these at intervals on the ice dam. The salt will melt down grooves for the water to flow.
As far as the "Problem", consider the ways heat gets there. This isn't theory, this is basic laws of physics. If you can't figure out why the attic is warm, hire a professional that specializes in heatloss problems.