Gas Fireplace and drafts

[RoadRunnerNews]

I have a relatively new house ('05) that pretty much stays cold all the time even with the heat on 76 it still feels cold (crappy Centex home). We have a gas fireplace that we really don't use, but I noticed that a good bit of cold air comes in through the grate right under the fireplace, this is the place where the gas hose comes in and the pilot light switch is located. Any suggestion on keeping air from coming into the home from the grate?

Also, there seems to be cold air coming in from the floorboard/baseboard area how can i reduce that? I hoping to sale this place ASAP.

[Nexus7]

Does anything else such as the water heater or furnace share the chimney with the fireplace? Probably does, since you have gas to the fireplace. You could install a chimney cap, and check the siding/brick & mortar on the exterior of the chimney.

Is the siding or brickwork on the exterior in good shape? If you see holes, a temporary fix would be to pump some expanding foam (for example, Great Stuff) to seal them.

Once obvious leaks are sealed, the remaining biggest win is to check if you have enough insulation in the attic.