craftgrrl | disguising a burnmark in a hat?

I accidentally left my jacket over a lamp the other day and it started to melt...I was lucky nothing burst into flame, but it did burn through the bottom of the jacket and into the pocket, where I had a wool hat (which also got burnt).

Basically, now I have a jacket that looks like a bite has been bitten out of it at the bottom (fixable, by means of a patch, I think)...but I'm wondering what to do about the hat...there's no hole in it, just a big ugly brown charred mark on the bottom edge. does anyone have any ideas about how to creatively disguise it? (It's one of those beanie hats...brown with a blue stripe along the bottom).