Fill a pantyhose leg with calcium chloride -- CaCl2 -- ice melter from your local hardware store.
Tie off the top part of the pantyhose with a tight knot. Double the knot to further secure it.
Lay the stuffed pantyhose on your roof so it is on top of any ice dams and slightly overhangs the gutter. The pantyhose should melt a channel into the ice and snow to allow the water to drain away safely.
Leave the pantyhose on the roof until the ice has melted underneath, then move it to a new location if there is still calcium chloride left in the hose.
Fill pantyhose with more calcium chloride and repeat the process if there are still areas that need de-icing.