Actually - I have seen technical reports thar state that wool, of the lighter weights, wicks better and regulates the body temperature better than cooton. For this reason light weight wool is better than cotton in a hot climate....
In the "Malayan Emergency" some British forces ditched their cotton shirts in favour of the wool shirt as they were better suited to the heat and humidity....
This is absolutely the case -- there is almost nothing a person would want in clothing that different wools can't be great at. In my view, wool is the most "technical" of all fabrics.
And happily wool still keeps you warm when wet too.
Between wool, silk and linen (another super material that gets too often overlooked) all of ones outdoor fabric needs can be well met.