As long as the TV is properly, correctly and firmly fixed to the wall, then it will be mechanically fine. My concern would be that hanging anything above an appliance which is designed to get hot (eg a fire!) needs very careful consideration. A TV generates its own heat and needs to dissipate that heat by cooling down. Hanging it in hot air won't help.
It all depends on the nature of your fire, the fireplace, construction of the walls, distances, sizes and all the other factors that I know nothing about.
My suggestion would be to hang a thermometer on the wall where you're thinking of placing the TV and turn the fire on for an evening. If the area above the fire gets somewhat hotter than the rest of the room (or above 30 degrees Celsius) then I'd think again. Actually, I'd remove the fire ;-)
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!