For those who have never had birds, it is very normal for them to sit with slightly spread wings and pant a little, in heat. Your budgie, parrot will do the same, it is best to focus on their habitat being shaded and well provisioned with water bowls. Other measures may not work so great when power goes out, you have to go to work or attend to family matters or emergencies elsewhere.
My personal opinion is that a wet towel is better than ice cubes - I am from very hot climates in the southern hemisphere and I never give cold ice water to people or animals, especially when they are in heat distress. Hikers "sip" ambient temperature water because it takes less energy. However it depends entirely on your set up -what works for a flock of 6 is not the same for a flock of 100.
My personal opinion is that a wet towel is better than ice cubes - I am from very hot climates in the southern hemisphere and I never give cold ice water to people or animals, especially when they are in heat distress. Hikers "sip" ambient temperature water because it takes less energy. However it depends entirely on your set up -what works for a flock of 6 is not the same for a flock of 100.