Purchase snow-melting tablets, widely available at hardware stores. These tablets are specially formulated to melt snow upon contact.
Stand several feet away from your roof's edge and don protective gloves. Toss up several snow-melting tablets, aiming for the spots where the snow is heaviest.
Use pantyhose to hold the tablets in place, if desired. Insert a snow-melting tablet into each foot of a pair of pantyhose and tie a knot in each leg about 6 inches up. Insert a tablet above each knot and tie another knot to keep the tablets into place. Alternatively, fill each leg with calcium chloride pellets, available at hardware stores, and tie off the legs to keep the pellets in place.
Tie a piece of string, about 10 feet long or longer depending on your roof height, around the crotch of the pantyhose.
Grasp the string in your non-dominant hand and don't let go. Hold one leg of the pantyhose in your throwing hand, twirl the pair above your head to get momentum and toss it up on the roof. The pantyhose should land with the legs apart, spreading out the tablets or pellets. Pull the pair back down with the string and toss again if you don't like where the pantyhose landed.
Climb a ladder if you must to place the snow-melting tablets. Wear boots with good traction and ask a spotter to hold the ladder for you to avoid falls. Climb only as high as necessary, steady yourself and toss the tablets into place.