Check out LL Bean for cool max t-shirts for about $20. I started with two of these in the sleeveless style when I started biking. I've since had to move on to jerseys with back pockets for longer rides, but I now use these t's for yard work and/or tennis! They are awesome and totally feel like cotton...

The first three items on this page are all cool max:
http://www.llbean.com/webapp/wcs/sto...at=ssdpa500653

You may also be able to find similar stuff at a local TJ Maxx or Marshalls or some place similar.