Well, the heater in the garage didn't work, so we caved and called Dennis, the plumber who moved the pipe in the kitchen. He's downstairs now, hooking up a gadget that will send an electrical current through the pipe and melt the ice. He said we're very lucky the pipe didn't burst (something we knew, but I don't think we'd really considered all the damage that might have been done to our as-yet-unfinished kitchen).

Dennis also pointed out some things we could do to help keep the pipes from freezing again (though he did say that weather this cold was unusual for Philadelphia—it only happens every 5-10 years), including getting some new weatherstripping for the garage door and doorframe, and insulating under the garage soffit. He pointed to some gaps under the soffit that I never noticed before (ding! it now becomes clear why the basement is so cold). We also need to let the faucets drip tonight—it's supposed to go down to 5 degrees again.