In order to run the Add-on, you also need to have the console on.
Is this creating terrible wear to the console or is it fine since it is not really using processing power as it would for a game.
My console is hot after a movie, but not terribly hot.
Im well vented and have not had an issue yet (Fingers crossed).

As long as you dont have a defective part and its well ventilated, you'll be just fine.