They wouldn't call it Burning Man if there weren't a lot of fire around.  While the olden days of Burning Man had a lot of unregulated bonfires, we've learned since that this leaves burn scars on the desert that last for years.  So you don't see that sort of thing as much now.  But there is a lot of fire art, as sculptures and performers.  Of the 30,000-odd people there in 2003, an estimated 1000 were fire performers.  I was one of them, though not an artist of the level of some of the shows I have witnessed out there.

(Click on the thumbnails for a larger image.)
 
A flaming gazebo, full of drummers.  It's hard to explain, but this sort of thing just sorta blends in out there.

A flaming fountain, fire and water spilling down through several tiers.
Then there are the fire dancers.  This one would be, um, me.  Sorry, vanity shot.  That's the moon in the background.  It does look pretty cool, doesn't it?
A shot of an elaborate good-vs.-evil tale performed in a dome by a group called El Circo.  They had amazing costumers and aerial work melded into the show.
This was the opening stage of a heraldic fire performance in 2003.  It was performed simultaneously on the side I was sitting and on the opposite side of this structure.  My interpretation was that these are the evil priestesses, summoning their minion.  
  Here, some of the forces of good confront the summoned creature.  A 4-legged stiltwalker, very cool looking.  
  I don't want to give the impression most of the fire performing is so elaborately staged.  Often it's just some people off in the desert.  Here's a shot of some of the Death Guild crew.  They also stage mock battles in this dome styled after the Thunderdome in Mad Max 3.  Industrial music, opponents on bungee cords, foam clubs, and the audience clinging to the dome chanting the line from the movie: "Two men enter!  One man leaves!" (or some humorous variant).