From the SRD:
FAST HEALING
At the beginning of each of the creature’s turns, it heals a certain number of hit points (defined in its description).
Unlike regeneration (see below), fast healing does not allow a creature to regrow or reattach lost body parts.
A creature that has taken both subdual and normal damage heals the subdual damage first.
Fast healing does not restore hit points lost from starvation, thirst, or suffocation.
Fast healing does not increase the number of hit points regained when a creature polymorphs.
It doesn't mention anything about fire (or acid) damage not being healed, like in regeneration. I've always thought of fast healing as a "lesser" regeneration. So does fire damage heal with this ability?