We went to primary school without - hell even my High School (private grammar school) still didn't have air cn through most of the school! lol
We survived perfectly, yes it was hot sometimes...but honestly it was fine.
That was in Melbourne

We don't have air con at home and now we live in Perth! I would think though that if I were sending Charlotte to school HERE then yes, Air Con would be important - it was 30 last week and that is almost winter lol It is not uncommon for 35+ degree days in October so, ys it would be more of a consideration.

But in Melbourne, whether her school has air con or not will not a priority at all.
And they are probably much healthier NOT having air con