This might work - picked up from another site:
Hi there, removing a burn from a carpet is nearly impossible I did have an iron burn on my carpet. I found a dog brush (a small brush with small wire bristles) and pick it. This fluffs the carpet, also a razor, a cheap BIC razor. go over it LIGHTLY start 4 inches away from actual burn and do it very lightly towards the burn so it blends in. If you have any more questions I am handy on fixing carpets (what can i say I'm a klutz, I spill and drop a lot of things!!
Hope that helps some.