Earlier quoted context omitted.
You do not understand the issue at hand. Whatever you experienced was way less severe, because evaporative cooling obviously was still possible. There is a point where you simply cannot cool yourself passively. That's the point where survival is at risk regardless of health. https://en.wikipedia.org/wiki/Wet-bulb_temperature
Having a rag of cold water on you will cool you regardless of evaporation. It is a thing that is cooler than the environment. The water from our taps at least is a pretty constant like 50°F
I could imagine that a place where the nighttime temperatures are in the mid 30s (°C) would not have any cooler water available.