The Arc’s operating temperature is listed as between 32°F to 104°F (0°C to 40°C) - so I would put a thermometer where you plan to place the Arc and leave it there with the gas fire on for a few hours and just ensure the temperature (overall) is not going to reach the limit stated, bearing in mind that the Arc itself is going to get warm too whilst playing for some hours, so measure its temperature aswell with a laser thermometer and add the temperatures together. I would aim for an overall temperature of no more than 30°C to keep things well within the limits stated.
That said, I personally would not want to use this type of setup myself as it sounds a little unsafe to me and I think a good many people might advise against such a placement. Same goes for the TV too.