(I’m in Tennessee on vacation, walking everywhere. Many sidewalks just end, no crosswalks, etc. biking here would be dangerous)
I am 43, I have no chronic disease, but I would be afraid of more than just sweating if I went on a biking trip in that temperature. Sometimes I feel unwell even when walking in such heat.
If I stay at home and walk around I have troubles breathing when it's over 35°C, I have been several times on the verge of fainting when it lasts a bit too long over that temperature.
But I don't have a problem biking at that temperature or above. I've ridden for hours in temperatures near 40°C with no shade. As long as I get plenty of air, it's OK: it lowers the temperatures and I can breath. I mean, I prefer if it is 15°C lower :-), but it feels much better than walking.
Now in such circumstances you'd better not get caught in a climb, when your speed drop under say, 8 mph, because then you don't get any wind, while being on max effort. That's horrible. It happened to me once in a small mountain pass, on a road which looked like it had been painted black to make things worse. I had to climb down the sharp slope on the road side as I could, to find the shade of the few bushes which were around and stay there a few minutes, because I felt my temperature was rising way too much. Never again.
My 1st day out jogging, I could only go 0.5 miles non-stop before I almost passed out. Today I can do 5.5 miles non-stop. My cardiovascular system is in the best shape it has been in a long time. And I'm almost 60.