fill it all the way up with logs maybe with the ends facing out, might give you both insulation and a good look

Is the damper closed? You could install a gas insert there.

If you want to remove it they make fireplace balloons. You put it up the chimney and blow it up then close the damper. We have it our downstairs fireplace that we don't use. Or you could take out the unit and spray paint it with a brown heat resistant paint to blend it into the brown stone. Lovely fireplace.