Well, you'll need to get your lighter socket repaired/installed, then ...
... and then you can try something weird, per my suggestion. I noticed that a small electric blanket I recently purchased uses only 140 watts.
So I was thinking one could use a small inverter, about 300 to 350 watts, in the car, to power a blanket or throw-warmer. It's a bit oversized, so the idea may not be practical, but keep the idea in mind, and keep your eyes open.
Aren’t there some in the 175 watt range? 350 is a lot of overhead, not that the efficiency is likely to suffer much. But it’s more than you’d want to pull from a lighter socket.
I plan to get the lighter thingy in the next day or two, but thought of going to Camping World to see if they have a 9V heating pad. I can pull up the website and find out, or make a call, as there are two of them here in the Valley, one about two miles from here.
Either way, I’ll let you know how it all shakes out. I think if my bottom were warm, I wouldn’t be so miserable doing my errands.