Good question; one I've thought about for my room a number of times. If I could put my screen over the fireplace, it would solve a lot of problems, like better placement for my speakers on either side of the fireplace, and like better seating options, where the seats can face the fireplace and the TV at the same time.
Check to see how hot the wall gets. Some chimneys are well-insulated and don't heat up the wall over the fireplace significantly. Alternatively, you could put some kind of thermal insulation between the wall and the screen. The challenge would be to make the insulation effective but still aesthetically acceptable, e.g., make it look like a picture frame.
Make sure you have appropriate drafting whenever you have a fire. (I assume you might want a fire from time to time, although you never said so.) Alternatively, you might have a mantelpiece that effectively shields your wall from carbon fouling. Check the wall now and see if there are significant deposits. If so, consider cheap ways to make the mantelpiece deeper, like putting a wide board across the top. Experiment and see if this stops the carbon deposits.
You need to feel good about the screen height. We have all seen the magazine ads with the screen over the fireplace. Unless you can sit far enough away, you will be looking upwards at the screen. This would be like always being forced to take a front row seat at a theater -- your own! Personally, I like looking slightly downward at a screen, and my old direct view that sits on its dedicated pedestal is perfect for this. Good luck!
