Here in Nebraska the months between the dangers of frostbite and heatstroke are few. We are hardy folk however, and it doesn't keep some of us from riding through it all, though I do prefer those in-between months. The five minutes it took to take off winter gear is now used cooling down and mopping up, so it's all the same in the end. I sweat in the winter when I'm riding too, but obviously more copiously in warm weather.
Just what is it about sweat that tends to freak people out? Is it that it looks like you've been working? Outside? That you might stink? Is it “unprofessional”? That last one is what my husband was told by his boss in the 70's when he arrived to work by bike. I hope we're past that now. Besides the perceived issues with sweat aesthetics, there really are potential problems with coming in to an over air conditioned (in my view) building from the hot outdoors well dampened by your body's attempt to cool itself. Yes, if I come in directly to start work looking like Mother Of Swamp Beast people do look alarmed. My blouse may be soaked entirely through to the skin, I may have a wet saddle print emblazoned on my behind. It's happened. I sometimes have a tight schedule and I have to power through to a distant appointment at top speed. These circumstances require thinking ahead. If you don't have to worry about arriving business casual or looking calm, cool, and collected, you have it made. If you have a shower at your disposal, count yourself as in commuter heaven. Many keep clothes at the office to change into or bring them along. There are even special suit panniers for that purpose. I'm giving advice especially for those who can't/don't change upon arrival. For you there are baby wipes or a possible pit-wash.
Clothing: If I know I have one of the above days coming up, I like to carry a change of top or an over-blouse, deodorant (my friends swear I don't stink, but you never know), and a small micro fiber towel. Actually, I always try to have the towel handy. I also wear a very light and airy white shirt during the hours of 10 to 3, but more on that later.
Prints hide sweat more than solids. You may find you like a layered approach. Sleeveless or short sleeved top to ride in, light blouse over when cooled down. This hides any sweat on first layer, as well as keeps you from getting chilled. If your bra is soggy, you might change that at some point, if you know that to be a problem and you've packed one. If you feel you're getting chilled by the over-air conditioning that can be a factor. Your clothes should be, of course, light weight and somewhat loose if you're trying to stay cool. Wicking fabrics are great in the winter, but in the summer especially, they hold odor so I do wear a lot of cotton. If it's thin I find it dries out fairly quickly. One thing about light colored pants, however. I can NEVER keep bike grease or dirt off of them, even when rolled up.
Hydration and sun care: Unless I know I have access to water or a shorter commute I always try to keep water with me, even just for errands. It can also be handy for wetting down the lightweight cotton shirt I commute in when the sun is strong. When it's ridiculously hot I wet the shirt down under a faucet or with a water bottle and put it on. Instant air conditioning that lasts 10 minutes or so, until it's dried out. If you're out between 10 and 3, do use sunscreen on the places not covered up. You may be surprised just how soon you're having to have those funny looking spots frozen off otherwise. Besides, I think it actually feels cooler to not have the sun directly hitting your skin, as long as the over-shirt is loose and light in color and weight. If I'm riding during those hours and not working I just use sunscreen and not the shirt.
Hair: Keep it simple and off of your neck. I know some like dry shampoo. I keep it back and tolerate a certain amount of helmet hair.
Most importantly experiment and find what works for you. Don't let sweat or the fear of it stand in the way of you enjoying your commute. You sweat less when riding slower so you might opt to just allow yourself more time to savor the trip and arrive less damp in the process.