I went into a bike shop in a neighboring city. I have been looking high and low for an earband that actually works well under the helmet- not too hot, not too cold, not to thick, and certainly with thin edge wraps. I haven't found anything anywhere, with the closest to what I'm looking for being the Smartwool earband. Then, I go into the bike shop and Voila! I find an 'Endura' brand earband. I bought it for $12. Later, I searched on-line and can't seem to find anything about this earband, though it seems to be a UK brand.

Let me tell you, I have found the holy grail of headbands! It is comfortable, fits just right under the helmet, keeps my ears warm, and my head doesn't get too hot because it's uncovered. I don't even notice it when it's on, though I do notice my ears stay warm. Fantastic! Exactly what I've been looking for!