Fan and AC are essential. Monitor the ambient temperature of the room when the weather gets to extreme ends. At night you can have a window open in the same room, provided their cage is very secure. If you can make the room dark enough without covering the cage, then don't cover it.

Offer them the opportunity to bathe in or out of the cage several times a day or just give them a dish with water in at the bottom of the cage that they can go in. With misting, if they're not fluffing up then they are likely not enjoying it, and it's something you have to condition many birds to get used to and enjoy anyway.

Make sure you change their water more frequently when it is hot, and offer them chilled water and chilled foods (fruit and veg).

The ice bucket is a great idea too.