That's a good point that I didn't consider. While carbon fiber itself doesn't burn (it's interesting to look up the government's Material Safety Data Sheet on it), the resins definitely have different temperature ratings. As an example, I found a carbon fiber hood for the NSX in which different resins are available, rated for continuous service temperatures ranging from 250 to 350 degrees.
Also if you add resin to the search when looking up material safety sheets, you'll find a bunch of product-specific entries and all reactive properties of those products are related to the resins (except for high electrical conductivity, which is a property of the carbon fiber itself).
Either way though, it wouldn't be feasable to use as a coating.