I've never had any trouble keeping my core warm on the bike, even riding in the 20s. But my extremities do get cold. Your arms aren't really doing a lot on the bike and really catch the wind.
Makes sense. I ordered a long sleeved baselayer top by Icebreaker. I'm skeptical (by nature) about wool's wicking abilities, but the enthusiasm for wool in this group convinced me to give it a try.