Draft in Fireplace

I have a gas fireplace and I have noticed a large amount of cold air coming in through the fireplace into my living room. I want to know if there is anything I can do to fix this. The fireplace is a prefab and I have glass doors in place. I have heard some people mention that you should see if you can close out the vent. However, I do not believe this is the case for me. I was thinking of getting a magnetic cover to close off the bottom grill when not in use. Any other ideas/suggestions would be appreciated. Thanks.

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