I think it might be visually jarring to have your camera suddenly snap over somewhere else when you get revived, and that's probably why they chose to do a "fade out, fade in" effect to smooth the transition. Maybe it's also somewhat symbolic of your character's fade into unconsciousness, then waking up somewhere else? I suppose they could do a smooth camera pan over to the new location too, but what can I say, the fade to black just doesn't bother me.
Just walk out of the fire, then. When you are revived, you are temporarily invincible for a few seconds. That invincibility goes away instantly if you use any abilities, but you can still move around. So, best thing you can do before getting back into the fight is wait for someone to heal you up before you even think of attacking anything.