Spring time works wonders on ice dams.
If this is a continual problem, you might want to consider those electric heat wires. My old house had them but I never used them because that wires were so old and scary. Too bad those kinds of things have to be up there and exposed to the sun year round. I wonder if there is some kind of temporary kind a guy could put up. Probably wouldnt work so well ON TOP of the ice.
David, long term you might want to take a look at your insulation/ventilation to make sure its adequate. Usually ice dams start because of escaping heat to the roof, melting the snow that then freezes when it gets out over the eve. Stop the melting (less heat escaping/more insulation, more ventilation to keep the attic as cold or near as cold as the outside) and you'll have little to no ice damming.
I once heard it described as an illustration that in a perfect world, a roof would be up off the house and 100% open on the sides. That gives you an idea of what you want up there. Cold air. Of course, the sun is going to still melt snow. Depends too on if you have a lighter color roof or if its dark. Be careful climbing around up there. Cold shingles are slippery! We dont want you falling off into a shrub or anything like that.