The short answer is that Wet Bulb Temperature  (WBT) can kill us cycle tourers if it is above 35°C. The WBT story as told by a satirical but scientifically accurate cartoonist known as “First Dog on the Moon”

In the US, the "Feels Like" temperature or Heat Index is more commonly quoted by the professional weather guessers - I think it is roughly equivalent to the wet bulb temperature. "Feels like"/Wind Chill is the winter equivalent.

I kinda feel like those numbers are mainly used by local TV "Storm Centers" (what used to be called weather teams) get more air time - in particular the Wind Chill, which seems mostly relevant if you regularly go naked outside in the winter...

But before those heat/humidity warnings were routine, years ago  during the week long Cycle Across Maryland tour on a century ride day MD's on eastern shore the last 40 miles after the lunch break were through air temps of 95F/35C with high humidity, no shade and heading southwest into the hot wind. Riders were dropping like flies or abandoning at rest stops.  These days that would be a start early/get done early/carry more water day - or only have the metric century ride. Climate change has meant we get 50% more days over 90F now compared to the long range historical average.

John I can’t ever recall cycling in extreme humid heat, which is why it surprised me to learn how deadly it can be. I’ve often cycled in high temperatures… 38°C, 39°C and even up to 42°C which eventually brought me to a halt. But these high temps (common in S.E. Australian summers) were in a relative humidity of 5% of lower. Evaporative cooling via sweat and a water soaked jersey worked well to unload heat when humidity was low. 

I doubt whether I’d last long cycling in your southern states summer humidity. I’d be bunkering down in an air conditioned building or dozing under a shady tree.