Don't wear businesslike attire when bicycling in hot weather. You pack it, instead, and ride at a comfortable pace instead of doing speed-racer stuff. Pack a thermos of ice water to drink from occasionally and you won't even break a sweat.
Or use an e-bike so you don't have to pedal as hard.
I live in the Boston area and I see a ton of people in business attire riding bikes.
I commute by bike daily in Austin, TX. In the summer I bring a change of clothes and wear a damp athletic shirt and damp headwrap. My commute is relatively short as well. I don't shower when I get to work and most of the time I smell perfectly fine. (Confirmed by people who have no problem contradicting me.) Yes, you'll sweat, but nowhere near as much as most people think you will if you plan it well.
Humidity would make this more difficult. Austin's not as humid as Houston, but it's not a desert either.
Or use an e-bike so you don't have to pedal as hard.
I live in the Boston area and I see a ton of people in business attire riding bikes.