I’m considering purchasing a wood burning hearth fireplace stove that would extend about 21 inches in front of the fireplace. Presently there is no issue with my widescreen LCD TV when the fireplace is in use. My concern is that the top of the stove could be used to heat something placed on top of it so would the heat generated from the top of the stove without anything on it, distort the air enough as it rises in front of the TV to impede viewing the TV. The bottom of the TV would be above the top of the stove about 26 inches and there is a mantel above the fireplace so the TV is not directly above the stove.
This page indicates that there should be nothing flammable above a wood stove to a distance of 1.5m (59"). A LCD TV probably won't catch on fire, but it could melt or have electronics break.
In short: bad idea.
I have put a flat screen above the mantle of a wood stove, I never noticed any distortion from heat but it did reduce the life of the sets. The first one only lasted about 2 years, the last one made it almost 4. I have other larger flat screens in my home and none of them have failed as soon. I suspect it is the heat, but in this room this is the best location because of a pool table. The newest one is 4K and I don’t see any issues with that screen.