A parrot in heat distress is easy to see.
They will hold their wings away from their body to allow air underneath for cooling.
They will also pant (breath with beak open).
Assume that your bird has not got done flying. It it's just sitting there doing those things it's feeling too hot.
Never had a problem up to 85 deg F but I would think giving them a mist bath would help cool them down.
Commonly, a good thing to provide your general region in this huge World as heat is different in different places. Example: Hot and Dry or Hot and Humid Heat! Two very different types of Heat that one needs to react to differently.