Size of Mantel Needed to Protect a TV
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Indeed a tv mounted over a fireplace is not ideal for viewing comfort.
There are minimum clearances that must be observed for safety reasons.
As you can see the further out a mantel protrudes the higher it has to be.
The question becomes “how far out from the wall will my tv protrude?
That will determine how far a mantel will need to protrude to deflect heat away from tv.
For reference the front of my 2016 era 65” inch Samsung on a full motion bracket sits off the wall about 9” when fully retracted.
If over a fire place I would want at least a 12” mantel to deflect the heat.
If you are determined to have a tv above a fire place you can see that the center of a large screen will be well above  the optimal height of approx 42” from floor.
However many TVs are set higher than optimal and if your room is large enough to allow seating far back from the fireplace the viewing comfort is not as adversely effected as in smaller rooms with high mounted tv.
Edit I just re read your question and see that your  mantel is stone so not a combustible material.
You could probably get away with a smaller clearance from top of fire box to bottom of mantel.