How sensitive are flat screen TVs to heat?

My family wants to get a flat screen TV for my parents this Christmas. The problem is that they want to put is near my parent's wood burning stove.

I think this is a bad idea. That sucker gets up to 700 degrees sometimes. And it obviously rediates alot of heat.

So, how sensitive are flat screen TVs to heat? All kinds, LCD, Plasma, DLP...