I commute to work about 4 miles each way by bicycle, in Dallas, in August. It was 104 here last Friday, and ~85F by the time I arrived to the office, but I don't sweat too much getting to the office. I wear typical business-casual riding in to the office, leave my shirt + undershirt untucked, and unbutton the top button, then tuck everything in when I arrive. I use a fan for when I first sit down but most people aren't even aware I cycle to work. The ride home on the other hand is a bit warmer. In London it's about 58-65 degrees at 8am in the summer, which is absolutely perfect weather for a commute of up to about 10 miles over flat ground. Most metro areas (seattle and SF excepted) are built on relatively flat areas compared to the surrounding terrain. Showering before you leave for work instead of the night before helps too, as you're very clean and slipping in to almost sterile clothes so stink isn't an issue going to work. I wouldn't cycle from work ten miles after work straight to a date, though.
But yeah if you're a fat couch potato who's grossly out of shape, you're going to have trouble not sweating, at least for the first two months until your heart and body regain some strength. The first two months of commuting were not ultra-pleasant but now that I'm back in shape with a strong healthy heart, 3-7 miles on an empty stomach in the morning (without coffee, even!) is a snap.