I can't really cite any federal or United regulations, but a heating pad on an airplane just seems like a bad idea. It's not that they regularly burst into flames all the time, but that the consequences of it happening on a plane would be so much worse.

I also have some concerns about the power supplies drawing such a large, continuous resistive load. Those empower adapters have made me nervous the last few times I used them, buzzing and rattling sometimes when I just have a cell phone plugged in.

Maybe just consider bringing your own extra blanket? I don't think we could guarantee that the TSA would even let you through security with it.