I agree with finding shade, etc. My quail are in my garage, it stays pretty cool, especially with either the side door opened, or even the whole garage door - they are shielded from the direct wind, however. Even so, I often notice several panting like they are hot later in the day, and it really isn't very hot in there. They always have water, of course, and they are always in the shade.
Keep the quail out of direct sun - or at least provide them with a well ventilated area out of the sun as part of their cage/environment. I am keeping chickens for the first time. Their run and coop are facing East, but it is up against a building, so they only get the morning sun. Luckily we built an elevated coop approx 2.5' above the ground. They spend the vast majority of their time in the shade, under the coop...I guess I would too if I was wearing a down coat! We are often cloudy and most likely a lot cooler than where you are in Texas.