What about countries with political strife like Myanmar? We can't hope that 100% of countries all experience significant growth, fast enough to outstrip the impact of rising temperatures. There will be laggards stuck on low GDP. Also, a lot of these economies rely on outdoor work, widespread AC can't help with that.
If we get to the 3-4C warming scenarios, these countries will be terrible to live in, regardless of AC, and I won't blame them when they all try to escape to colder Europe.
Air conditioning can get radically cheaper to meet market demand, and they can start making radically more money.
Other products have gone from expensive to cheap (think TVs over the last 40 years), other people have gone from poor to prosperous (think China).
Do you have a good reason why these outcomes are possible TVs and for Chinese people, but not for ACs and equatorial people?