Unlit Mithril fire arrows are used during the Underground Pass quest. They are created by using a damp cloth on regular mithril arrows. The arrows can be lit by using them on a fire to create lit mithril fire arrows. The lit fire arrows can pierce the rope in the Underground Pass Dungeon to lower the bridge. This is necessary to complete the quest.
Mithril fire arrows have the same Ranged Strength bonus as regular mithril arrows, and the fire provides no additional benefit.