I have kept out of this debate as I lack enough experience actually racing my birds. But perhaps I can tell some things from personal experience. When the birds open their beak and pant , it is too hot Imo. If flying for long distance they are deprived of water, and may land and drink as they need to which delays the bird. They also take longer to recover. I’ve noticed if my birds just loft fly, they pant at 80 degrees and over.
So what temp is too hot? I would say if you are hot, then so is your pigeons. It is said the most comfortable temp is 70 degrees for humans, I think pigeons can take a bit warmer so my opinion is they should not be crated up and crowded and forced to fly and get dehydrated in degrees over 80oF .