I live in Austin. I ride my bike as long as it's less than 100F (38C) out. Anything above 90F (32C) is pretty hard for me to do without getting sweaty. Fortunately, my office has showers.

Also, I think your advice to ride at a moderate speed is a good one. When I first got into bicycle commuting, I was reading the bicycle subreddit and I was told more than once that it never gets easier, you just get faster. Well, they were wrong. It gets way easier. I understand what they mean by "you just get faster", but I think it's potentially discouraging to new out-of-shape riders like myself.

It gets way easier and for me is almost meditative. My mind wanders like crazy.