may i put an hdtv over a fireplace?

Why sure you can. Don't listen to the above posters. They are just jealous cause they never thought of it before. I bet most of them are hanging their's above the fireplace as I type, just trying to be the first to post how they love the way their new flatscreen looks over the fireplace. Well they may as well forget it, cause I was the first. I wasn't going to let anyone else know about it cause I wanted to be the only one to have such a novelty. Yep, got mine hung up on the wall over the fireplace with thumb tacks, the center speaker on the hearth and the fronts on the mantle. For rears I mounted some good in wall speakers in the lampshades on each side of the couch. pretty nifty huh?
Now if you didn't catch that bit of sarcasm the answer is No No No

Pretty good rcprince.
I think it would be OK with a gas stove as long as there are no great heat problems. I would have it built into a sealed enclosure though for aesthetics, and to keep out smoke and lessen the heat. You could also have this enclosure somehow cover the screen when not in use.

Maybe you could just project a live video feed - people will think it's a mirror.

I've got better idea:
It's OK to me to hang it above the fireplace if you're not going to use it as a fireplace. Instead you could use it as component compartment.
But MAKE SURE that EVERYBODY knows that this isn't a fire place anymore!!!!!!!

No. Unless you have bleachers in your living room. If not you will have stiff neck, everytime you sit down. As far as heat goes, how many days in a year is there a need for fire, unless you live in Alaska. Isolation material behind and under the flat screen should take care of that.