Closing the flue to your chimney will help prevent the warm in the room from escaping up the flue. You should have glass doors to stop the air from escaping in addition to closing the flue.
The problem is that flues are not sealed properly. Over time they can warp and not seal correctly. One way to seal it up would be to install a chimney balloon.
Chimney balloons come in several sizes and is easy to install and use. You take it out of the package and unroll it so it will be easy to inflate. Begin to inflate the balloon, but not all the way yet. Before putting the balloon in the chimney, check to see if there are any screws or sharp edges sticking out. The balloon is very tough, but sharp objects can puncture it.
Once it is clear, slowly inflate the rest of the balloon. You want the balloon to be firm, not tight like a drum. It should have some give to it.
The manufacture gives you a red card that will remind you that the balloon is in the flue. The balloon will burst if lit, so it will allow smoke to go up the flue. The red card can be left hanging from the balloon, or placed near the glass doors or on the grate of the fireplace so you remember to remove it. Once you are done with your fire and the flue is cool, you can reuse the balloon.
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