I think it could be done with enough imagination...you could fight fires, then rummage through after in a to find the cause, as the game progresses your character realises that there's an arsonist behind it, maybe he'd leave clues or letters, maybe it has something to do with a loved one who died in a fire and you saved someone else when you could have saved them...then the end would be a battle with the arsonist, as he lays fires and firetraps to try and kill you, preferably he's captured you first so he can have conviently pre-laid traps as well as traps laid on the fly.
There'd be melee bashes, at first to use against panicing civvies to carry them out or bust through windows etc...then they could be used against the ONLY bad guy in the last mission. It would be mainly puzzle based, how to get from a to b and back with the victims...moral choices of who to take and who to leave...and it could be 3rd or 1st person, probably best to be able to switch between the two. There could be fire "enemies" I suppose, say backdraft, and the like, certain visual cues to tell you when something is going to fall or the fire is going to bloom. Not in a "Flame, thirty second gap, flame" kinda way but in either set pieces or random areas, if you open a door the rush of air feeds the flames, you could try escaping out the window, but there's a chance it could kill your charges as straight out as the flames...
Also, it would need amazing fire and fire damage graphics.
I'm imagining something along the lines of Portal to be honest. But just because it showed how you don't need enemies in every room. Sometimes the room is the enemy.