I find I use the same clothing that I use to Nordic ski, which is a medium weight merino wool base layer zip-t (I use Ibex - ibexwear.com since they are here in Vermont) and a soft shell jacket. I find this combo lets out the moisture best and keeps me dry. Most likely the reason you are feeling cool on stopping is because you are getting wet from sweat while riding, you need to vent and allow your body to rid itself of moisture.