What would it cost for an electrician to add a receptacle?

The cost can vary. In my house I have firebreaks (2X4 in the walls running between the studs). They make running wires up the walls a little hairy at times and an outside wall is likely to be full of insulation. As for the heat from the fire place he may have a point because electronics doesn't like heat. It would shorten the life of the TV.