What temp does the room get to?
Do you have external blinds?
We have hot summers here on the Med. Last year we got to 44 - 45 C.
But in the house is not as hot as outside, usually.
We have all windows and doors open UNLESS there is a hot breeze, then we close all the windows and drop all of the blinds making sure the holes close.
We use a few fans pointed towards to patio doors to push the hot air outside.
We have a portable AC unit, we use it during flight times in the summer, I drop the blind and leave the holes open, and keep the doors wide open. I turn on the AC so the room temp drops (it is not as good as a mouted AC so it helps lower temp, but the room never gets cool).
The birds don´t get to be out most of the day like in the winter. I put them back for sessions before getting them out again so I can lift the blinds - especially if there is a breeze.
Each day is different.
I keep cool baths available inside the cages, and change water often to keep it cool (not ice cold).
Edit;
So in September I had my doors like this, open as fully as possible but blinds are down you can see the holes are open because it's hot but not hot wind:
View attachment 298616
And one month later in October the weather had cooled down so I used the blind to block sun and the door is closed:
View attachment 298615
When the wind is hot (like when you open hot oven) I close shutter completely so no hot air can enter.