It turns out that this is quite common but by the time one can get an appointment to see a doctor, it is gone. The unofficial name is Golfer's Vasculitis as they do most of the complaining but it is also known as Three Day Walker's Rash, Disney Rash, Epcot Rash, etc. To get it, one must be over 40, it must be hot, and one must be walking for at least 3 hours.
All of these conditions existed as we walked around San Juan for 5 hours. The redness is due to broken capillaries. It did not itch but it burned for a day or so. It felt hot to the touch. Pictured above is a poor picture (again, my friend will have a better one). I am surprised that I got this given my good cardiovascular system (can run for 90 minutes without stopping) and veins (I never have had a varicose vein in my life) but there you go.
It is now a week later and there is no sign of it on my legs.