Older masonry fireplaces may or may not have been installed with a damper to prevent conditioned air from leaving the home.
If your fireplace is one that does not have a damper, several options exist. Below are a few of the options starting with the least expensive.
Flue balloons are sold online and come in a variety of sizes to fit the opening (smoke chamber) just above your fireplace. They are a simple design, you inflate them in place inside of the fireplace and deflate and remove the flue balloon when you would like to use the system.
This is the least expensive option and it works rather well considering the cost. Be sure to remove the flue balloon before use, it will make a horrible smelly mess if caught on fire.
Top mounted damper
I will be the first to admit that this is not my favorite design when it comes to dampers. The damper is mounted at the flue termination up at the roof of the home and is controlled by a cable that runs down the flue liner and into the firebox. When you would like to open the damper, you release the cable and the damper springs into the open position.
The pros of this system are that it creates a good seal of the flue system when not in use and prevents most wind driven rain from entering the flue system.
One of the cons are that the mechanism can stick over time and not fully open and the damper is located on the roof so you may not visibly be able to see if it is fully open or closed without going on your roof.
The second con is that the cable can stretch over time and also must be removed in order to perform a proper chimney sweep.
Throat installed damper
A traditional damper is located just above the fireplace firebox. The downside is the cost of installation to have it professionally installed but it is also the longest lasting and most reliable option of the three.
The important thing is that multiple options do exist and you can even use a flue balloon as a temporary fix until a permanent damper is installed.