I use this reflective insulation. It is kind of like a bubble wrap sandwiched between two pieces of tin foil, but it's stiffer.

I cut it to fit inside the windows of my Element, which has convenient sunken windows which allow the insulation to stay up there with friction. That would be hard to do with a rental car.

So I have another idea based on what I do with my sunroof. For my sunroof in the hot summer, I put a piece of window screen on top of the car and hold it down with little magnets. You could do the same thing on the outside of a rental car. Carry a tarp or even just fabric pieces, cover the windows from the outside and put a bunch of little magnets around them to hold them down. You'd likely want them to be waterproof, since it would be no fun to have soggy fabric to put away. There are some parts of some cars that magnets won't stick to, so that might be a drawback. But you should be able to at least hang them from the top.

Think that would work?

Karen