The solution here is to just provide enough cooling methods I would say. I feel putting this in a wider ‘capitalist and climate’ frame is a bit overdone.

in what way? Saudi Arabia is already so hot (and at times humid) that going outside at all is potentially lethal--in no small part because it is a capitalist petrostate whose existence is predicated on cheap oil warming the planet--which also renders much of the Hajj literally impossible to do in any safe manner since it must be done outside. the climactic and capitalistic ties are fairly obvious here to me.

also, it's worth noting, the article explicitly notes one problem (of several) with your proposed solution:

Technological adaptations such as air-conditioning do work. But they are not available to all. Nor are they fail-safe. During a heat wave, many of us turn on the aircon at the same time, using lots of power and raising the chance of blackouts. Blackouts during heat waves can have deadly consequences.

Well, you're free to your opinion on that one.

What kind of cooling methods specifically should be implemented here?