Yep, summer weight wool baselayer (underwear), will do wonders. As others said, you can't really avoid sweat unless environmental conditions are ideal and you're not exerting at all. The wool will get it off your skin and keep it from getting "ripe" as it evaporates. I understand that in the old days wool underwear was ubiquitous. I guess the age of air conditioning made us forget why.

Cotton works just fine up until a certain threshold of sweating, beyond that it just gets clammy and uncomfortable.