draft from unused gas fireplace

[covener]

I have a gas fireplace installed in an external wall, and during the winter there is a pretty significant draft from vents both above and below the fireplace opening.

The bottom vents are removable, and I see what appears to be an open space sitting on my concrete slab.  The area behnd the top vents isn't really accessable.  The flue is closed.

What I believe is the "cold air vent" on the outside doesn't seem to be adjustable; if I have no interest in using the fireplace is there efficient way to kill that vent?  Is there any use in filling in the area between the slab and the unused fireplace? 

I do plan to shove one of those inflatable balloons up above the flue opening because it seems relative inexpensive.

I was told by a savvy contractor that it wasn't worth pulling things apart to see if there was adequate insulation on the exterior wall.  His suggestion was some type of air-tight glass in front of the fireplace opening, but looking around I only see costly/relatively elaborate doors for the front of the fireplace.

Any suggestions appreciated!