I'm not saying the tour riders are wrong, but the standard practice in ultrarunning is to put ice in your hat (usually wrapped first in a bandanna). Seems like a simpler solution.
BTW, St. Louis set an all-time high today of 108F.
108F? In St. Louis? That's disgusting!
Wouldn't the Arch melt and sag into the river, causing steam to rise and raising the humidity well past 100% and maybe even into the 200% range, in those conditions?
Pretty sure stainless steel holds up to 108F without any problems.
...and probably also 108 C... (when you definitely would want not only one but two ice hats).