May one ask gentile to turn down or off gas to stove or grill on Yom Tov?
It depends why he is asking him to do it. If there is a Yom Tov related need, such the food will burn, of the room is too hot then it is permitted. However if it is just to save on the gas or money then he may not do so.
The reason is because it will be a shvus d’shvus (a double drabonon) when there is a need or in order to do a mittvah, ( that the food shouldn’t burn). see HIlchos Hamoadimchap. 9-6, The laws of Yom Tov pg. 103. Whikle it is true that if the food might burn even a Jew can make the flame lower, but he would not be able to do it if it is merely to cool down the room. In this situation a gentile may do it for the above reason.