When a room is on fire, the quickest way to extinguish the flames (so that it credits the "extinguish fires" objective) is to have the room filled to capacity with non-pregnant dwellers.
Powerful guns + high Perception work to reduce the amount of time that radroaches and mole rats disturb a fully-occupied room.
Given a fully-occupied room on fire, besides maintaining occupancy, are there additional factors which reduce the amount of time it takes to extinguish a room fire? Perhaps stocking the room with dwellers who have a specific high-value SPECIAL attribute?