I can confirm that it's very possible to burn in a car with the windows up. I burn on my arm and thigh closest to the window when on road trips. It's enough of a problem that I now wear long sleeves and long pants if I'm going to be in the car for hours. I don't burn as fast as if I were sitting outside in the sun, but I absolutely burn.
As far as heat penetration goes, I also find myself adjusting the climate control depending on whether the sun is shining on me directly or if I'm shaded by the roof.