I played 36 at Saucon Valley Old and Weyhill back in 02 in the middle of July, walking, and wearing pants as i was told I had to. We started early, but it was well over 90 (with very high humidity) for most of the day. My two friends and I counted that we each drank 18 bottles of water or gatorade, and one of them still felt sick and had to lie down after we finished. Luckily the club's pool is about 20 yards from the 18th green at the Old course, as we were in it 90 seconds after putting out.
The no shorts rule is pointless, the only thing that can happen is someone is stupid, doesn't drink enough water, and passes out on the course. Forget tradition, its just common sense.
I think "no shorts" rules are kind of stupid but I really can't imagine that the difference between shorts or no shorts is going to make the difference in passing out. The day you referred to you probably would have suffered just as much in shorts.
The club can make whatever rules they want, and as a guest I can decide whether it is worth it to play there if I find the rules particularly stupid. Maybe if a club has a rule that first time visitors have to wear a propeller beanie maybe I say "screw it" and don't play. Or if Friar's Head tells me that, maybe I put it on and say, "let's get the pictures you wish to blackmail me over with now so I won't be distracted on the course"
If shorts really do make that much difference, you should lobbying for courses to let you play shirtless or nude when its really hot out. If shorts help you stay cool, no clothes at all should help even more. Plus it would be easier to play out of water hazards.