Official Blizzard Quote:
Diablo: Every fire explosion the FX guys create is the best fire explosion we’ve ever had in the game. I think they’ve got a competition going.
First off, we have to consider that the existing mage classes ( Witch Doctor and Wizard) have a minimum of fire skills. The Witch Doctor has several of course, but the explosions for Skull of Flame have already been completed, or so I would assume since it was shown in the first gameplay demo. Pit of Fire is also a fire skill, but I can't imagine an explosion coming from a roiling pit of flames. I could be proven wrong of course, so don't quote me on this.
As for the Wizard, they have no fire skills. They have Arcane, Lightning, and Cold, but as of now we've yet to see any fire skills used by the Wizard. I highly doubt the Barbarian will have many explosive skills, however the Monk may have a couple up his sleeves.
Now, if the FX team is doing so much work on flaming explosions, we have to ask, where are these going to fit in?
Of course, they could be doing work on skills used by monsters (remember the Catapult back in Lord of Destruction?), or perhaps some traps. However, my money is on this becoming a significant part of the fifth class. Right now, the majority of people speculate the fifth class to be some form of ranged class. Thus, if we look back upon Diablo II, we already have a ranged class who used fire, being the Amazon. She even had a skill called Exploding Arrow, which was followed by Immolation Arrow, both ranged fire skills that featured an explosive animation.
Now, I'm not suggesting they're going to recycle the skills from the Amazon, but right now, I would put money on the fifth class featuring some wicked looking explosions.