Shuttle Atlantis, with Carbon Damage Underneath and on Leading Edges, From Wikipediathis. Crimeny, 1000 hours of exposure? A well ridden bike could see that in a year or two? Does that mean a carbon bike will die due to the sun after such a short time?
Well, actually, there's some good news here. Most carbon bikes are also painted, at least in some areas. The paint suffers due to UV. The tires suffer due to UV. The brake cable housings suffer due to UV. YOU suffer due to UV. In reality, UV is one of the things you really do NOT need to worry about when it comes to your carbon bike. If the paint is fresh looking and you don't have skin cancer, and you aren't storing that really expensive bike out in the sun, it WILL probably survive UV longer than you will, and probably your children as well. The shiny finish probably has UV-resistant chemicals in it, and even if not, the shiny surface will go before those strong fibers even notice.
OTOH, if you want to use your bike as a replacement for the Space Shuttle, and subject your bike to reentry while exposed to high moisture, you ought to be very careful about UV, and rapid oxidation generally. Likewise if you have a wooden bike that you leave out in the sun. If the shellac/varnish disappears, the fibers are getting attacked and termites may follow.
Consider this article a "whew, I'm glad Steve made me feel a little better" day. For the sun, the paint will go before you have to worry about the carbon. Next the epoxy will go, but even then the carbon fibers will be as good as the day they were cured into the epoxy. Just you worry about impact!
If it makes you feel any better, my road bike is now 12 years old, and I have absolute confidence in its carbon front fork. Of course, the frame itself IS aluminum, but pay no attention to that man behind the curtain...