I do think it is wise to choose one's route based on the level of heat/humidity. While my short rides are 20-23 miles regardless of how hot it is, it makes a massive difference if it is within the hilly but quite shaded nature park across from my apartment complex, or the flat country roads though the corn fields with no shade at all.

I have asthma, and I've yet to have any problems with heat and humidity while riding as far as the asthma is concerned. I seem to be far more sensitive to colder weather in this department. My allergies even seem to have disappeared since I started riding!

I also have given myself permission to not ride if the temps exceed 95 or if the heat index breaks 100F. Depending on conditions I can still ride in the park in those temps, but if it is just too oppressive then I won't. We don't NORMALLY have too many days where temps get higher than that - if I lived elsewhere that would likely have to chance if I wanted to ride regularly. The important thing is to acclimate your body to where you live