You can mount an LCD TV over a fireplace without damaging the TV. But there are other reasons why mounting in such a place isn't necessarily a good idea.
Heat and soot can damage a TV placed over a fireplace, but this is relatively rare. As long as the area around the television set is less than 37.8 degrees Celsius, it should not damage the television set. Soot damage can be avoided by turning off the television set before cleaning the fireplace. If the set is left on, the static from the TV might attract soot that is kicked up during the cleaning process.
While it may be safe for the TV to be mounted above a fireplace, it is certainly not easy. HDTV Magazine writer Richard Fisher says it is not an easy job to do on your own, and will be expensive to pay someone else to do, if you can find an installer who will do it. Many reputable installers refuse to mount a TV over a fireplace due to the difficulty of the job and the potential for things going wrong.
While your television can be mounted over a fireplace without getting damaged, your neck might not be as lucky. Ideally, a television set should be set at eye level when you're sitting down. Any higher can cause neck strain that can make long-term viewing a painful experience. Julie Govan, writer for Crutchfield's online store, says that mounting an HDTV over a fireplace will cause painful eye and neck strain. Furthermore, she says it's a bad place to mount a TV because it will be outside of its optimal viewing angle, making the picture darker and muddier.