Fair enough. This is the kind of cyclical process without discontinuities, so it will follow the average.
However, for things like animal migration - and generally the more immediate threats of climate change, such as increasingly destructive weather events, ecosystems dying out, crops failing, wet bulb temperature hitting levels that make some countries uninhabitable in the summer - tracking the high and low points matters much more. E.g. the average may even go down, but if this is because cold point drops and high point goes up, ever for a small part of the year, we can kiss farming in the region goodbye.