I've searched the forums and wiki for this, but I find conflicting information. Perhaps someone from Three Rings could give us a definitive answer.
When you acquire the Fire status, you periodically take damage. What is the type of the damage? Elemental? Normal? A mixture? Some typeless damage? And does armor protect you from this damage?
Normal. The damage pips are red.
Most armor would protect you roughly equally from it, so you won't notice much difference from any set without fire resistance.