Fill tube socks with snow-melt granules. Stuff them full until you get within 5 inches of the ankle opening. You will need one sock for every 2 feet of roof line. Tie off the opening of each sock after you fill it.
Remove the snow on the roof with a roof rake. This will make the sock come into direct contact with the ice, so you won't waste chemicals on melting the snow.
Place the socks perpendicular to the roof line, jutting the toes of the socks 1 to 2 inches out over the edge of the gutter. Place one sock every 2 feet.
Leave the socks to sit on the ice. The snow melt will seep through the sock material and melt the ice dam underneath it.