http://wiki.answers.com/Q/Are_diamonds_flammable Says diamonds are combustible around 1520 degrees.
But temperatures were 1000 degrees at the high-point in the 9/11 events (page 10 end of first paragrah): http://eagar.mit.edu/EagarPapers/Eagar185.pdf
Interesting enough. The bigger issue would have certainly been the buildings crumbling before they ever burst into flames/disintegrated.