We have a flat screen on top of our fireplace, because we live in a loft, and there really isn't any other place in our loft to put a TV (for our family area). We had a really cool fireplace facade built which created shelves underneath the TV for our cable box and DVD player. I am more than happy to post a pic of this so you can see if this is something that's doable for you. Let me know and I'll do it when I get home from work tonight.
Otherwise, so far (and we have lived there over 2.5 years) and haven't had any "melting" or overheated equipment (knock on wood). I guess it just depends on the fireplace facade/unit. Ours is natural steel so it's very thick and sturdy. It isn't that high, and the TV isn't mounted on the wall but standing on the TV stand on top of the fireplace facade. We also have a gas fireplace, so maybe that makes the difference, as well. IDK.
I hope this helps.