It's not the end of the world if someone arrives at work with a bead of sweat on their forehead.
Sweat occurs on most forms of transport:
1) Walking on the streets, red hot pavement, wearing a black suit, sunshine radiating heat down on you. There's no getting away from it, you're gonna break a sweat, whether you like it or not.
2) Encased in a train carriage, windows that only open about 3mm, sitting next to some fat bloke whose blubber spills over to rest on your thigh. Yuk!
3) Standing, squeezed in to an underground tube train, your face buried in someone's sweaty armpit, conditions far worse than animal transportation rules and regulations. But don't worry, because London Underground tell us repeatedly the status is a "Good Service". Hmmmm.
4) Even private vehicles, for all their expense & pollution, are still just rolling greenhouses. Surrounded by glass, a car's air-conditioning battles against the relentless power of the sun. Ironically attempting to cool the global warming effects, which its pollution contributes to worsen.
So regardless of what transport you choose, if it's hot, everyone is going to sweat anyway.
With regard to cycling, whether you sweat or not is completely within your control:
Exertion - Sure, you can push hard & fast where appropriate, and you'll be more likely to sweat.
If you prefer, it is entirely possible to not even break a sweat on a bike. Select easy gears up hills, cruise at a leisurely pace, and freewheel effortlessly downhill.
By constantly moving through air when cycling, you experience a kind of natural air-conditioning, continually removing any heat from your skin's surface. This helps cool riders down.
Clothing - This is not so much about buying expensive cycling apparel, but simply deciding the appropriateness of what to wear, evaluating each day before you set off.
E.g. Underestimating the temperature and overdressing will cause you to sweat unnecessarily. So a little check of the weather forecast, and perhaps a cross-check with your own thermometer before setting off, will guarantee you embrace whatever temperature, suitably dressed.
Distance - I often find that my body doesn't warm up or generate much heat for the first 10 or 15 minutes while cycling. By this time I may have already covered 3 or 4 miles. So the shorter your journey, the less of an issue body heat is, and vice versa.
Why does sweat get such bad press? I think it's because people associate it incorrectly with smelly B.O.
Now herein lies the difference: Yes, an unhealthy, overweight person excreting a diet of chips, booze, & fast food through their pours, probably does emit an unpleasant stink.
BUT a regular cyclist, typically; healthy, fit, with a reasonable diet, is more likely to be giving off those sexually potent pheromone signals, rather than anything comparable to Mr fatty!
Showers provided by responsible employers clearly eradicate the sweat topic completely. But the point of this article on sweat is that everyone does it, and it's not a problem. Plus the fitter you are, the less you sweat anyway!