Not too expensive, I already have one set and they are great in the summer for keeping me cool, and preventing leathers or outer garments from sticking to your skin.
If by "not thermal" you mean not designed to keep you warm, then I suggest lightweight Patagonia Capilene. Amongst other Patagonia garments, I have a long sleeved, zip top. lightweight base layer and matching long johns. I've worn them extensively, under my Belstaff / BMG Adventure suit when riding in temperatures of 40 deg C plus in the US.
It's lightweight, breathable, very quick drying and comfortable. It's not exactly cheap though....