There are several discussions on here about the subject, and the answer depends on what type of fireplace you have, how close the TV is to the fireplace and whether or not there is a mantel shelf between the fireplace and TV.

The bottom line is that your TV warranty probably says not to install it near a source of heat, so you are in uncharted waters. There are no set rules about TV clearances, other than the clearance to combustibles listed in a manufactured fireplace installation manual, and those are just about preventing fire, not about protecting electronic equipment.

The installation shown above, with a cast stone mantel shelf between the direct vent gas fireplace and the TV, should be fine, but TV recesses tend to build up heat instead of letting it disperse. As many designers will suggest, the TV is a little high for comfortable viewing if you are siting close to it.