I do not know what would be worse.
Not having air conditioning while cooking an entire feast, or not having heat while trying to enjoy the big feast! I feel it is safe to say that living in a sizzling region, during the Fall weeks, neither of these events would be much of an issue.
The region where I live is mostly warm in the Fall weeks. We don’t have a furnace. There is really no need to have any major heating equipment. If it gets even sort of cold, I do have heating equipment other than that. Although, I feel the people I was with and I could manage. One thing the people I was with and I could do is light the wood burning fireplace. So many homes in this region are made of brick as well as have a wood burning fireplace. Although not really used, the people I was with and I try to use the fireplace any chance we get. Having the heating method break down on a major holiday would be a good excuse to light a fire in the fireplace. My family keeps space heaters in the home for guests who might get chilly in the middle of the night… Personally, I do not like to sleep with any kind of heating device, but I do prefer the look of a space heater first thing in the afternoon. A holiday lunch would not be ruined separate from a heater. It could actually be a fun thing to experience with your family, as well as even make for a good story to tell for years to come.