But, yeah, I wouldn't be happy putting a TV above a fireplace, no matter how good the flue was. You're going to get heat, you're likely to get (at least some) smoke and ash. Not good for the longevity of the TV.
I'd never put a TV above a fireplace either, but the heat/smoke/ash stuff just isn't true, at least not for our fireplace.
The wall above our fireplace doesn't get noticeably warmer* when the fire is lit, I've never seen any smoke escape the fireplace and there is no ash on the mantelpiece. In fact the brick around our fireplace are painted with perfectly standard household paint and even the ones that butt up against the firebricks in the fireplace itself have no heat or smoke damage.
* this surprised me a lot when we first converted our fireplace back to a real fire, I did expect the chimney breast to be noticeably warmer when the fire was going