Although it looks nice, mounting a flat panel TV above your fireplace can take years off of its life if you aren't careful. Aside from possible smoke damage, your new LCD or plasma screen was built to run at a specific temperature (check your owners manuals for exact specs, but usually between 32-100°F), so watching a movie and building a roaring fire can actually damage the components inside your TV if it gets too hot.
Thankfully, all is not lost. Find out how you can ensure your new TV doesn't get fried from the inside out after the break.
If there's no stopping you from mounting your set, there's a quick test you can do to find out how hot your fireplace will get. Attach a thermometer to the spot you've chosen to mount (tape and a cheap thermometer from a drug store will do the trick), build a fire, and let it burn. After a few hours, if your chosen spot is getting close to your set's maximum operating temp, then you shouldn't burn the fire and watch the tube at the same time, or choose another place for your TV to call home.