Hanging a TV above a wood stove?
Code aside, the hottest thing in our living-room after the woodburner itself is the area directly above the wood-burner. I don't think this is a good place for any electronics, as most electronics generate heat of their own. Typically they dump these using heatsinks (large lumps of metal that quickly spread the heat over a wide area, like a radiator on a car or in your home), but these rely on the ambient temperature being relatively low. You'll find the electrical circuits in your TV will have a MUCH shorter lifespan - nevermind what it would do to the screen itself. 

To be sure, check the manufacturer's recommendations for siting the telly and you'll probably find a safe operating temperature range. Compare this to the temperature of a thermometer hung where you want to hang your telly.