If you are going for a faster performance run / racewalk, think best to employ DIY ice packs with cubes/slushies on towel and in your running vest pockets. Can go taobao buy the soft water flasks, which would also make contact with your body. The towel hang on your neck. Optional, cap with ice slushie packs inside.
The water dripping onto down onto your dry-fit would then evaporate.
The somewhat low RH% would make it work one.
Last Sat i cycled at 4.30pm on rail corridor to buy makan from ABC Brickworks hawker, bought wow wow west western food.
Was very manageable even at relatively high speeds. (ok dont tell authorities lol....barely any sane fellas that time). 1 way 11km there, my totally wet Hoka top already like mostly dry coz of the self-generated wind.
Then prior to the way back, took out my top and again totally wet it at the toilet sink before riding back.

Somemore my Hoka top is black in colour, still very manageable....but is coz cycling (wind wrt effort) + latent heat of vaporization.
If running during hot afternoons/evenings, i sure overheat for 10k, been there done that.
So....dont take such risks unnecessarily, prep for it.
ps of coz if just take part for fun and run-walk-run-walk, it would be fine....coz you would self-regulate. Risk is more of the athlete's mindset, push even though it is becoming dangerous. The active cooling is more of a safety net, and of coz improves performance.