When I play softball (or any sport) I prefer to be as scantily-clad as possible. Well, let me rephrase that: I don't like a lot of layers of clothing dragging me down. This could be because my core body temperature is higher than the average person, meaning I get hot and sweat much easier. Anyway, I wear sleeveless jerseys or tank tops whenever possible. I have found, over the last eight years, that I just can't swing a bat effectively if I have sleeves or any kind of undershirt.
However...I was recently convinced to buy and try an "Underarmour" shirt. This is a fabric, widely-used by athletes, that wicks out moisture in hot weather and insulates the body in cold weather. I was dubious, but after an hour of practice with a sleeveless underarmour shirt underneath my jersey, I found that not only did it keep me cool, but I didn't notice it was there.
So that's my advice on this April Fools Day: if you do sports or exercise and haven't tried this product (or one like it) you should. Highly recommended. Their web site is www.underarmour.com/