Good luck, I know its a worry, I had the same thing last year with the Adelaide heatwave.
During hot weather I hosed the aviary roof down after I had laid towels to stop the water draining off. I also hosed the walls and the canvas blind down too, it acted a bit like an air con.
Other quick solutions could be raiding trees or palms for leafy branches and putting them on the roof and against the walls and wire, anything to create a bit of shade and then hosing them down.
I even went as far as putting in large ice blocks in the planters, the birds loved them, the minute I was out of the aviary they gathered around the ice block taking advantage of the cooler area, watered the plants too!