...It seems with doors open and the temp around 75F it would be hard to melt a hole in the fabric from reflection.
Actually, it's pretty easy, given the size of the reflector. Consider that you can fairly easily light a piece of newspaper on fire using sunlight concentrated through a 4" magnifying glass with pi*r^2= 12.6 square inches of area. If you have a much larger reflector, say an 15"x15" window with about 225 square inches of collection area, the focus doesn't need to be nearly as precise to achieve ignition temperatures.
...I was thinking it was focusing of the light through a window. Either way I now need to come up with some placards to hide the marks.
Constant-thickness transparencies such as airplane windows make pretty poor refractors, unless the rays are pretty close to tangential. And then you lose a ton of area, and lose a ton of energy to reflection. One way to look at it is that if it were a better lens, it would be a worse window, with much more optical distortion as you looked through it. That's why I remain convinced that this is a reflection issue, not a refraction issue.
Sailplane pilots have gotten savvy about this problem, and are careful about where the glider is pointed while the canopy is open. They avoid orienting the glider so that sunlight can reach the concave inner surface of the canopy. Anytime that happens, there is potential for sunlight concentration to ignition temperatures.
As another poster pointed out, there is also potential for light to reflect off of the wings, onto the concave surface of the window, and then get focused to the upholstery on the door. That's an added complication that calls for a bit of vigilance when the doors are open.
Thanks again, Bob K.