First Question: Is it a gas burning or wood burning fireplace and do you use it?
Second question: How high is the mantle?
Third Question: Is there at least a cable outlet up there as well as a power outlet?
A gas fireplace won't generate as much heat above the mantle so the LCD panel would be "generally" safe from overheating. To test, start up the fireplace and place you hand above the mantle. Too hot for your hand? Then too hot for a TV.
Take a piece of cardboard cut to the same size as your prospective LCD TV and tape it to the wall above the mantle. Sit where you would normally watch TV and ask yourself "If I watch a 2.5 hour movie from here will my neck hurt from looking up all that time?" If the answer is yes then don't do it.
Finally, if all that's available over the firepalce is power, how are you going to get a signal to the TV? Don't even think about anything wireless......there's nothing reliable at this time. Is the wall above mantle brick, wood or drywall? Can you run wires in the wall in a DIY mode or will you need the aid of an installer. If the fireplace is wood burning you have other considerations as well. If it's gas then you have option to snake wires in the wall.
If answering the first two questions still leaves you with the urge to mount a LCD panel above the fireplace then I would HIGHLY suggest you consult a qualified custom installer (look in the phonebook under Home Theater).