Has been on my "to research" list for a while. I agree with you that Europeans should stop being so stingy with AC (speaking as an European who still hasn't an AC, but not much longer), but I do wonder how much they actually do to prevent heat deaths.
Because, how many heat deaths happen at home where people would potentially have AC? As far as I can tell (pre researching it) most, if not all, heat deaths I am aware of, happen outside. So the question would be: What is the effect of having a cool 22C home in regards to suffering heat deaths outside. Does it make it better, because your body can cool down? Does it maybe make it worse, because you step into a harsh difference when leaving it? (The last one is probably an easy no, since plenty of countries with high AC rate don't seem to have that issue).
(Or just general damages from heat, not just heat deaths)