At higher temperaturs we need more cooling, ok. But the big question is what is the relative humidity going to do? As the moisture holding capacity of air also increases rapidly with the rise in temperature, changing the equilibrium. The rule of thumb wet gets wetter, dry drier doesn't always apply. It's going to be quite interesting..

https://nicklutsko.github.io/blog/2019/03/22/Will_Future_Climates-Be-Wetter-Or_Drier