When not in use, close the damper.
Seal fireplaces that are not used (a makeshift foam plug can be inserted and then removed if you decide to use it again). Hanging a flag from the plug will serve as a safety reminder. Remember even a closed damper leaks a large amount of heated air to the outdoors.

Avoid having your furnace thermostat in a room with a fireplace.
Consider installing tempered glass fireplace doors and a heat-air exchange system so warmed air could be blown back into the room.