A problem, especially in the Summer, is keeping your cool in your brooks brothers while you pedal through 100-degree heat. Modifying one's clothes, at least for the ride, is one way to beat the heat. Another is to be flexible in one's schedule. There is no magic way to keep cool while riding fully clothed in the hottest part of the day. Bikes don't have air conditioning, wind helps but makes for harder work.
Prevention is the Best Medicine?
Instead of worrying about dealing with sweaty clothing, one can change his or her riding habits to sweat less. Leave earlier in the morning. Leave when it is cooler, even by 9 a.m. it is hot enough to cause problems. Assumedly, the ride home during the hot afternoon isn't as big of a deal because one is going home, where there probably isn't a dress code. Also, something that can be psychologically difficult, ride slowly! Pushing hard and going as fast as possible will cause more sweat. Sometimes, however, when wardrobe modification is not possible, this is one of the only ways to keep cool.
Be Lucky: Have a Job with a Shower
The easiest way to deal with biking heat is to be lucky enough to have a job with a shower. Some employers have an on-site gym and locker room. With this, it is possible to just ride to work in any clothes, shower at work, and change into fancy clothing after that. This requires transporting work clothes, but for more on that, see below. Also, not everybody is so lucky. If there is no shower, bringing a washcloth and whipping oneself down quickly in the bathroom goes a long way.
Don't be Self-Insulating
If possible, do not wear suit jackets, or other heavy, superfluous articles on the ride. Also, it takes a few minutes for one's body to cool down after the ride has stopped. Waiting a while after arriving before putting on the rest of one's clothes will stop the Costanza effect (George Costanza on Seinfeld complains about sweating long after he has stopped working out and even after a shower). If the dress-code at work is flexible, wear a t-shirt for the ride, wait a few minutes, then one can change into a work shirt, jacket, smock, or what have you after one's body has cooled off.
Transporting Work Clothes
I advocate not wearing heavy, hot work clothing while riding. This necessitates having work clothes either waiting on-site or transporting them there. If clothes are kept at work, get them cleaned somewhere nearby so they don't have to be brought home between wearings. If one has the luck to be able to store a variety of clothes at work, consider oneself lucky, but most of us will not have this luxury. A good idea is to transport a small garment bag. Do not be intimidated, I do not mean the large garment bags often brought on airplanes. Try to find a small tri-fold garment bag. I have one that came from inside a suitcase. This can easily fit on a bike rack or inside a good-sized back pack. See an upcoming post on transporting stuff for more on carrying solutions.
What to Wear
Although it sounds counter-intuitive, I have heard wool jerseys wick sweat away better than traditional synthetic bicycle jerseys. There are other synthetic shirts that are designed specifically to wick sweat off of the body (less sweat on the body, the less for bacteria to live in, the less smelly one gets), underarmor or similar types spring to mind. Some people like a handkerchief wet with cold water and tied around the neck to help keep cool.
On a non-clothes related note: stay hydrated. Not drinking water will not keep one from sweating less, it will be dangerous! So, drink water. Cool water will absorb some of your body heat, cooling down your core temperature. Some folks recommend insulated water bottles.
A review of a cooling vest.
A bandana to keep your cool.
Wool Jerseys and a review.