Try a Pearl Izumi Transfer baselayer shirt or comparable undershirt. I was skeptical about the claims for magical poly fabrics and was on the verge of ponying up for a merino wool jersey like I used to wear (I was tired of the clammy cotton t-shirts -- not bad in summer, but chilly and uncomfortable in cool/cold weather). But Nashbar had the Pearl Izumi on sale and I was already ordering a couple other things so I gave it a try. If you shop around carefully you may find a new-in-box old stock Pearl Izumi shirt heavily discounted -- mine is dated 2011. Supposedly they upgraded the material last year, but I'm satisfied with it as-is.

Over the past week I've ridden four or five times on days ranging from 40s to 70s, under a longsleeve cotton/poly jersey, a Shimano Storm Jacket (not very breathable), and just under a cotton t-shirt for walks outside at night in the 30s.

It works just as claimed. It's remarkably warm compared with snug fitting cotton. Yet it doesn't retain sweat and feel clammy, then chilly. On the cooler day when I wore the Pearl Izumi baselayer under a cotton longsleeved sweater and the Shimano jacket, after a 20+ mile ride with temps in the 50s the cotton sweater felt damp but the Pearl Izumi shirt was nearly dry and I didn't feel chilled.

This afternoon was warm enough, up to 70, for a ride with the PI baselayer under a very thin Garneau short sleeve jersey. No sweat, literally.

This magical poly/"minerale" stuff really is as good as claimed. I probably won't bother with merino wool again, although I have a nostalgic soft spot for the stuff.