From Diablo Wiki
Fire is one of the types of damage in Diablo III. It is red-tinted in appearance and leaves corpses scorched black.
Fire damage is dealt by a wide variety of character skills and can also be found on weapons. Though fire damage is merely orange/red damage with no special effect, there are a number of fire skills and items that can leave flames on the ground, dealing DoT to enemies within the burn zone.
Diablo III Damage Types
During development critical hits scored with fire damage were to set targets ablaze, dealing additional fire damage over time. This effect and all other elemental effects (save cold) were removed during development. A return of fire damage and other secondary elemental effects is likely in the Reaper of Souls expansion.