I would definitely be writing a letter asking why it doesn't have air conditioning and when they expect to have air-conditioning. It really is unacceptable not to have air-conditioning in a new building built in sydney where it is common to have at least a week of 40+ days.

I would include something along the lines that it is unfair to expect the teachers and children to suffer in that kind of heat and that your DD had heat rash yesturday. I would take pictures in future just in case.

I would even be looking at other options of childcare centres if you have options.

your poor little DD