My second thought is to stab some aluminum strips into the heart of the larger piles. Aluminum is an excellent heat conductor and is available in a number of forms at the local hardware store. If I can find some cheap strips (preferably black), I can essentially conduct heat into the heart of the pile. I could put them in in the morning and then pull them when I got home so they wouldn't cool the piles during the night. Not sure if they'd work, but it might be neat to try.
Jeff is soliciting technical suggestions on how to remove the snow. If you have any, you can write them in his comments section. Or for more fun, you could excessively complicated, expensive, and preferably dangerous solutions in my comments.
This is a contest. The most preposterous and/or reckless proposal wins.
One word: Napalm.
Multiple words: Napalm lit without the aid of time-delayed fuse. Instead, the source of ignition is a torch, which is delivered to the incendiary via an Olympic-style relay. Through bear infested woods.
Of the suggestions, I found this to be the most immediately dangerous, although there would be long-term dangers to smoking/eating Jeff's tomacco.