Leave it empty. It's a geometric design feature, not a ledge for piling stuff.

We have the same problem, yet the heat has never created a problem in the 10 years we have lived in our home. :) It's a ventless gas fireplace. We hang Christmas stockings every year. There is a small shield on our unit (see photo below), but it really doesn't help with the heat rising. The underside of mantle gets very hot! And while we do not have a TV above, there does not appear to be any overly high heat above the mantle. No obvious problems with the painting that we can see. Try putting a suction cup thermometer in the middle of your TV to gage the temperature. Thermometer Our problem is with the logs "off gassing" when we run it. Yes, we have have the gas company, several gas and fireplace techs, etc. our here, and they all say everything is fine and the off-gassing is normal. Our problem appears to be that the ceilings are only 9' high in our space and the off gassing has no place to escape. We cannot change to vented because of building codes and having windows within a certain distance from the vent. We have changed log size. Went from 36" to 30", I think. And have even turned down the gas intensity (which means that flames are lower.) None of this has helped the smell. It helps to open the french doors, but when it is cold all the heat in the house goes out. So we rarely use the fireplace. We are seriously thinking of putting in an electric set of logs this year. After 10 years, I am ready to have some sort of fire look without the smell. Our HVAC man is looking into one other option before we go ahead with electric. Anyway, I was getting off subject. Good luck! Black shield, right below the granite slab, slopes out and down about 6". Our mantel is high and about 12" deep. Gets hot, and before we changed the log size, some soot would gather underneath. Sold the previous logs, with no problem, on CL.

You'll want to switch all your bulbs for LEDs in the 4K range to improve the light and the way color reads in the space. I would match the mantel to the trim color, or paint it a stricking black to match the firebox surround and hearth. Also plan to style it with fewer items and replace the mirror with art, since it is not reflecting anything beautiful or interesting you'd want to see twice.

Aside from mantle decor: The lower half of the fireplace below the mantle is narrower than the upper half. It looks off balance and top heavy. The Emerald Green tiles sound lovely but they would accentuate the asymmetry. To remedy that, I would remove that 3-4 inches of baseboard on the angled section on each side and clad that vertical strip in your tile from wood floor to wood mantle. The upper and lower halves would be the same width. You could then even bring the tile floor-to-ceiling. Wouldn't that be spectacular? Then decorate mantle with white items to stand out.