Can I arrange with a non Jew before Yom Tov to turn off the oven during a Yom Tov?
The halachos of asking a non Jew to do melacha for us is the same on Yom Tov as on Shabbos, therefore since we may not tell a gentile before Shabbos to do melacha for us, we may not tell him to do so before Yom Tov. We may however hint to the gentile that we will need the oven turned off before Yom Tov, the same way it may be done before Shabbos.
Shulchan Aruch O:CH 307-2, M:B ibid 10, O:CH 517-2, M:B ibid 9. Although there is a prohibition to benefit from the melacha that a gentile does for us on Shabbos or Yom Tov, turning off the gas is not considered deriving benefit, as there is nothing that the gentile is actually giving here, rather he is only removing something, and permitted.