I haven't been on the Phoenix cam - how long was it between the time he fell and when he was brought back to the box? Long enough to get checked out by a vet? And shock is not something you can see on an exam or x-ray but it can kill birds later on.
Looking at the temperature forecast posted earlier on this thread, I think that would be a greater concern - peregrine chicks rely on getting all their moisture from the food their parents bring them, so dehydration would be a big concern. Heck, I worry about our chicks at the Radisson in the hot afternoon sun but fortunately, by the time the sun starts to really get hot in June, the chicks are able to move in/out of the shade in the box, their parents are good about providing shade and it fortunately doesn't last long and when it is gone, the chicks can hang out/sleep out on the balcony and catch whatever breeze there may be. And it isn't much easier for the adults, they can only pant to thermoregulate so they tend to hang out in the shade, preferably shade and a breeze or they end up having a bath somewhere which does cool them down but I can't say how easy that kind of bath might be possible in the Phoenix area ....
Hopefully there will be an update later ...