Is one allowed to turn off a gas grill on Yom Tov. It’s outside, so it wouldn’t be to stop a room from getting too hot. The food will be done, so it won’t be for the benefit of the food. Safety might be a small concern. I’ve heard that R’ Moshe allowed it, and I heard a rational for this because nothing is actually burning, like a wick or coal (just gas). I saw a similar question on this sight, but it doesn’t address this directly.
As your question so correctly implies, it should not be done on Yom Tov. there is a type of shabbos clock for gas ovens, which is sold in Eretz Yisroel, although i wouldn’t know if it isold in the sstates nor if it can be used on a grill.
Have a kesiva v’chasima tova