Can you vent your nestboxes so that heat can't build up and it's no hotter inside the nests than anywhere else?
Our nestbox lid is always propped open with a wood block during daylight hours PLUS we change out the solid winter floor tray for a ventilated wire-bottom floor during summer PLUS we special-built a patio roof over the coop for added shade and protection from heavy rains PLUS the girls are free-ranged in the backyard to pick and choose their favorite hangouts. -- shady trees, garden sprinkler, dog houses, canopies, roofed patios, shaded/canopied sand-bath, etc.
We even made make-shift benches for the hens to hide under for shade along the walkway and along the backyard block wall.