[0] https://en.wikipedia.org/wiki/Evaporative_cooler#Physical_pr...
Funnily enough I was thinking that about you, because on 40+ days we've got people out riding, overcrowding beaches, walking and some even sunbaking, many will be doing that without shirts on in the open sun and they're not going up in flames. Some poor buggers even have to work outside doing physical labor on such glorious beach days. Personally on days like that I like to go for a quick swim and spend the afternoon with a beer on a bowling green if I can. We've been doing this for generations, my great grandma was doing it before cars, sunscreen and aircon were invented and kids had to walk to school, indigenous people were doing it much longer. We aren't scared of the sun as our skin cancer rates will testify.
Of course these days there's people that take the doona off in the morning and enjoy their air conditioned house, run to their air conditioned car to work in their air conditioned office for 8 hours then do it all in reverse and never see the sun. Of course they don't climatise because they're living in a different climate.
The more wind you experience (or the faster you ride your bike) in those conditions, the more work your body needs to do for maintaining homeostasis via sweating. You will certainly not perceive a >39c wind as a 'cooling' wind in any conditions, and the faster that wind is the hotter it will feel.
The efficiency of sweating depends on rel. humidity. Not what's being discussed here.
The fact that increasing airflow will increase the rate at which you heat up (and how much heat your body must shed) if that airflow is hotter than your core body temperature is just physics 101. Why do you think fan-forced ovens have lower cooking times or temperatures in recipes?
The 'self-created airflow' INCREASES the rate at which you gain temperature. Windchill is only 'chill' when the ambient air temperature is lower than your core temp.
To cycle on a summer day, you need to slather yourself in SPF-40 sunscreen including underneath clothing, wear SPF clothing, and make sure to be constantly drinking water. And when you get to your destination you're definitely going to need a shower. I'll take public transport over that, thanks. So does the majority of people.