First of all, if your fireplace is venting properly, you shouldn't get ash/smoke in the house except when maybe lighting it. If the doors are closed, you should get a good vent as the heat pulls the air through.
Secondly, a mantle will diffuse more radiant heat.
Third, build a fire, even if it's hot outside..., good roaring one, hang a thermometer where you want the TV. Let's say it gets to 90 deg. (prob less) Look in the TV's manual. What's the safe operating and storage temp? If it's in that range, you're safe.
My chimney wall stay's cold even if I have a roaring fire.
Finally, LCD's are better than plasma. Go swap it out. Plasma's will burn out in 6-9 yrs of regular use, and LCD's backlight can be replaced. My brother's 60" LCD HD Sony Vega looks great
5.4 block from 99 expedition bored .20 over
Forged crank/Manley Rods/JE flat tops/chromemoly rings and Steeda Underdrives
P&P PI heads (by me) w/ 3 angle valve job w/copper gaskets with ARP studs/bolts and One piece lightning cams
80mm Pro-M MAF and Cut & welded '95 4.6 intake
Jmodded Trans & Trac-loc pumpkin (Cobra) 3.27
Raxles, ADDCO 1 1/4", Eibachs, JL Braces
18" CEC type 169 wheels w/ 245/40 front 255/45 rear