Should i mount a tv on top of gas logs fireplace

Well, it must have been the temperature. After I left the fireplace on without the logs for a half hour and let the whole stove get nice and hot, I turned the burner off, put the logs back, and turned it back on. It's been going for an hour now without any shutoffs.

Yes. These are painted all the time. I just used this for a traditional wood burning fireplace. You can search for fireplace paint but really you are looking for it to withstand the max temperature. Since yours is gas I am guessing your max is well less than 1000 F.

Also most fireboxes are painted black so you can see the fire easier. And because of the heat a lighter color may get burn marks in it from the heat.