Point taken about the electric blanket, the insulation can get brittle over time. I guess there is no inexpensive and completely safe portable heat source, even the furnace in the basement of most houses can fail catastrophically due to wiring shorts, gas leaks, or burner or boiler failure.
I can think of a few other ways to provide some spot heat. Topping off the charge on the battery is what I often do when snow is expected. The process of charging the battery will also generate a little heat, and give it a little boost too. A trouble light with an incandescent bulb shining up on the oil pan can provide a little bit of warmth, but make sure there are no oil leaks.
I did this one cold winter at my old house to keep the oil furnace going. I had an outdoor oil tank for my furnace, and the line running from the tank to the house had a slight kink in it. The kink wasn't really a problem until the temperature dropped below 20 degrees F, then the oil would congeal at the kink. I ended up taking a trouble light and with some aluminum foil to direct the heat I positioned it over the kink to keep things warmed up. Admittedly, this was a temporary solution, but I was only a couple of months short of moving into my new house, and I was renting the old place.