"The limit of the willing suspension of disbelief for any given element is directly proportional to its awesomeness." -- The Rule of Cool

Instead of starting discussions about the flammability of fur and the velocity of sparks, you should just enjoy the awesomeness of the picture.
This is a picture from a furry universe anyway, so there can be lots of creative explanations for everything: For example as a werewolf he could just regenerate any burned fur very quickly; there could be some dragon in his ancestry, giving him fire resistant fur; he could use fire retardant shampoo or spray; he could have sweat glands that keep the fur moist enough that singed fur is not a problem; or MAGIC!

Anyway - my LARP character is also a blacksmith - so here is a nice picture of him in action...

This amazing picture was created by latex ( https://www.furaffinity.net/user/latex ) for Rakan ( https://www.furaffinity.net/user/rakan )