You're overemphasizing that article's weasel hypotheses couched in weasel words: "may" "likely" "seems" "it is possible" "usually". T
That article then loses all its weaselness when talking about schools and human behavior (as opposed to the weather). The article then highlighted:
This leads us to the last point: Even seasonal infections can happen “out of season” when they are new.
If we're talking just about respiratory viral contagions (and not animal-borne diseases like malaria), then the main vector is human behavior. And the behavior of throwing all our snot nosed kids into the same building is the prime cause. And the seasonal nature of schools, leads to the seasonal nature of viral respiratory illnesses.
Here's another part of that article:
In the winter humans spend more time indoors with less ventilation and less personal space than outdoors in the summer. In particular, schools are a site of much infectious disease transmission. School terms have been strongly identified as periods of higher transmission for respiratory viruses including those causing chicken pox, measles, and flu (here and here). The 2009 pandemic flu in the United States was very much decreased during the summer, and then came back rapidly in September.
Highlighted in red is pretty much all the evidence one needs. September is not a cold month. It is the time when schools reconvene.
There should be zero expectation that warm weather would slow transmission of CV19. If that were the case, Iran and Australia wouldn't be having as many cases as they have.