I'd like to note that in '93 (maybe '92), the Rangers and Kings play an exhibition outdoors game in Las Vegas. The temperature at puck drop was around 80 degrees. If they could do it then, they can certainly do it now. So I don't think that climate will be that big a factor with regard to how warm it is outside (of course, in Vegas there was very little risk of rain, as there would be elsewhere).
Once the novelty of the game wears off a little and it becomes a well established new years tradition, a game in the desert might be fun change, especially if the Coyots continue to build a good young team. Sun Devil Stadium? I don't think it holds any bowl games anymore.