I wear light poplin shirts with no undershirts when it's hot, and I usually don't sweat all that much if I take my jacket off. Which I will do anyways if I start sweating, as dry cleaning after each wear is not an option...If you're not wearing a jacket, lower armholes on shirts help quite a bit too.
I don't know how hot it gets where you live (Madrid, right?), but wearing poplin is out of the question for me here. It may be light but, probably due to the tight weave, I find it 'breathes' a lot less than looser woven, heavier fabrics. So as a consequence the shirt will be soaking wet in a matter of minutes and then, yes, my jacket has to absorb the perspiration. Taking my jacket of is of course a big no no