Thank you all so much for the kind condolences, words of wisdom and advice. It's so nice to be able to turn to people who understand that chickens are more than just egg producers and a protein source!
Perhaps tethering your roosters is not the safest way to protect them from each other.
Janinepeters, you are probably correct. There may be better ways to keep them separated, but I can't think of any that are practical for me or I would do it. People who keep game breeds have used tethering as a common method of securing roosters for many years.
I suggest either moving your chickens away from trees with low branches or shortening the rope so they cannot fly high enough to perch.
Dolly85, you are also correct. However, a lack of shade in the hot summer would certainly kill every one of them! I left the branch there because it provided valuable shade for him. Besides, he's been under that tree for most of his life and he only tried to roost in the branch occasionally (meaning approximately 3 or 4 times, total). And this was not usually a problem because I am not usually away from home for more than an hour or two at a time. I work form home and can usually keep a close eye on my flock throughout the day. Yesterday was very unusual circumstances for me, and I wish with all my heart that I had thought to move him somewhere safer for the day!
The answer is YES. And I do know it to be correct. I have a friend who lost a rooster because he forgot to trim his spurs and he found him hanging upside down by one of his spurs in the morning dead. Chickens cant breath correctly when they are hanging upside down. Then all the added stress.....
Tiki244, WOW! That is just incredible! Maybe now I can finally say I've heard it all??????? I had pretty much concluded the same as you until I spoke with my Dad. He's been around awhile and he recounted to me how as a youth, he would deliver chickens to the market by tying their legs together and carrying them upside down by their legs the entire 4 or 5 miles. It would have taken him at least an hour or two to make the trip and he said the chickens were always fine. He suggested that perhaps my boy got up there earlier in the day when the sun was boiling down and the COD was heatstroke.
It seems the only way to know for sure is necropsy and I don't have the money for that. But, thank you all again for your input interest.