How do osprey cope with temperatures above 100 degrees? There are several things I have seen them do.
One is they sit with their mouths open like their are panting. There is a reason they do this. According to Couchiching Conservancy:
Birds have no sweat glands, so the primary way of dissipating excessive heat is by panting, just like a dog. If you see a bird during the hottest part of the day, it will likely have its mouth open. You may or not see that their throat is moving up and down, ridding heat from their body through the open bill.

Another way they cope is the mom will take short flights from the nest and go into the water to cool off. I have seen her float for a little while then fly back to the nest. So swimming or taking a dip helps them cool off.
In addition, when the mom returns to the nest after a dip she will shield her young from the sun under her wings. The nest is exposed, so she is shading them from the sun like an umbrella. I have seen the babies huddle under her wings.

Also, I have seen the mom flap her wings or stretch them out more as the temperature rises. According to Couchiching Conservancy:
Another method they employ is to spread their wings and body feathers which allows heat to dispel and cool air to circulate between them.
Like a crazy person, I stood out to watch them in the afternoon of the days the temperatures reached 100 plus. I brought plenty of water and did not stay near the amount of time I normally stay. Take precautions when out and about and have a great Sunday.