At our county fairs that are held in mid summer here -
they fill up plastic water or pop bottles and freeze them, then they lay the frozen bottle in the cage with the animals.
The animals will lay next to the cool bottle if they get too hot.

for the cows, pigs, horse and other large animals they have big fans in the barns and take then out to hose them off often.

the frozen plastic bottle is a good tip to remember for smaller animals & birds
you can put a few ice cubes in a shallow dish of water - in case your birdie wants to cool himself off