I would like to mount a 42" flat screen plasma tv above my fireplace. 
I have a woodburning fireplace with a wood mantle extending about 8
inches out from the wall.  If I have a fire in my fireplace will I
damage my tv?

This doesn't sound good:

http://www.plasmatvbuyingguide.com/plasmatv-questions/plasmatvfire_1.html#11109240

Will the heat from the fireplace harm the plasma TV?
There are a few precautions to take before implementing this TV
application. First, take a thermometer and tape it to the wall above
the mantel (where the plasma TV will be placed). Then and build a
fire, let it roar while. Check the thermometer. If the temperature is
above 90 degrees then the area is receiving too much heat - either
escaping from the front of the fireplace and rising up the face, or
radiating through the chimney to warm the outside wall. In this
situation it would not be advisable to run the plasma for a long
period of time while its environment is hot. Though the Plasma TV has
its own cooling system, the surrounding heat will force the Plasma TV
to work harder to cool itself, thus shortening the life of the unit
over time. The Plasma TV may still be run for short periods without
harming the unit even with the environment heat at 90 degrees or
above.

If the plasma display is not turned on during the operation of the
fireplace, then the unit will not be harmed at all even though the
temperature surrounding the unit may be warm.