Oddly enough, I stayed home yesterday to deal with frozen water pipes.

I am perplexed at these 'frozen water main' claims. I had three ice jams, and each was where the house branch line exited the ground (pipes are buried in the crawl space) and entered the crawl space.
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You troubles don't happen when the pipes freeze; the problems happen when thawing water has no place to go, and the pipes burst.

Therefore, I consider the 'welder' approach to be a good way to burst a pipe, especially if there are any elbows in the run.

Instead, I chose to apply GENTLE heat to the 'downstream' side of the ice, after opening the line. For heat I placed one of those oil-filled electric radiator-type heaters near the pipe, and used a small fan to blow heat toward the pipe.

Slow? You bet- but I managed to clear all three jams without any broken pipes.

Prevention, of course, is better than repairs. My (first ever) freezing pipe problems were caused, in part, by the fact that my home is undergoing some major remodeling, and not as much heat has been leaking into the crawl space as a result. Ironically, the issues will be permanently addressed this Summer, when I have a complete re-plumb scheduled.

In the mean time, I have sealed the crawl space much better, and have rigged up some low-quality heat trace lines.