Only issue for the badwater link is that it is for runners that can't go fast enough for the evaporative cooling effect to exceed the amount of heat they are producing. Cycling you can do that. Anytime I'm sweating and over 16 mph in high 90's to triple digits, heat isn't an issue. Slow down and/or stop sweating, then it's time to be alert for heat exhaustion.
Certainly everything in that article is as anecdotal as my statements.