It turns out that my fleece sweater alone isn't warm enough, so hopefully putting my windbreaker on over that will fix the problem.
Whenever possible, I prefer to stop at a pull-out of some kind rather than just on the shoulder of the road.
This preference has developed as result of past experience out here. Kind desert folks will often stop and ask if you need assistance if you look like you might be having a breakdown and are stranded on a shoulder. Of course, this is an excellent thing when one is actually in need of help.