Hey salt springer, I'm amazed to see your post as I logged on to ask exactly the same question! :-) I hope you find a resolution to your problem soon.
My LO is 8 months & used to sleep occasionally in the car seat, now she screams & screams until she is boiling hot & dripping with sweat. Even stopping the car, calming her down, cooling her off & starting again doesn't help. I used to think she was hot first and this caused the upset but now I'm not so sure. It's making journeys very stressful as I often drive with her alone and can do nothing while driving. It doesn't happen every time and if she sleeps then she doesn't cry - although she does still get very hot. I may well try a mirror but does anyone know of any cooling product/technique that could help? I have a modern car and use the air conditioning to keep the car itself cool but this doesn't help.