Short Answer: Linen for hot weather. Wool for cool weather. Cotton when temperature and performance is not an issue.
Linen is quiet different from other fabrics as it has highest heat conductivity and air permeability of any fabric. It actually reduces skin temperature, unlike other fabrics. You'll notice a lot of business attire is made of linen in the tropics and middle east due to the heat.
Heat conductivity of Linen
The rate a fabric transfers heat is referred to as its heat conductivity. Heat conductivity and air permeability combine to make a fabric feel fresh and cool. Linen has the highest heat conductivity of any fabric, therefore it lowers your body temperature.
Breathability of Linen
What governs a fabric’s air permeability is how rough or hairy a fabric is. A rough hairy fabric will trap air, slowing its movement and transfer heat. In the case of linen, the fibers are long, wide and smooth, which allows air to pass through with ease.
Wool is on the other end of the spectrum from linen. When viewed under a microscope the fibers appear hairy and erratic. This results in trapping air to form a means of insulation. The added bonus of wool is its incredible antimicrobial properties which means it can't be beaten for anti-odor. A wool shirt can be worn multiple times without generating odor.
Heat conductivity of Wool
Wool has low heat conductivity, so it will provide warmth. It's ideal for cold climates.
Breathability of Wool
As mentioned, linen fibers are hairy and trap air, which results in warmth. However, this can be viewed as a reduced air flow, not a restriction on air flow Wool still maintains a strong sensation of breathability, unlike synthetic fabrics. Modern manufactured merino wools have no itchy sensation like old generation thick fibered wools.
Cotton is a natural fabric that feels good in average temperatures. Cotton doesn't provide much warmth nor does it provide cooling. This is an economical fabric and therefore the most popular for dress shirts. Cotton's weakness is it tends to retain moisture when wet. If performance is not an issue, it's a great option and will offer far better breathability than any synthetic fabric.
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Wrap a measuring tape around your hip bone line, making sure the tape is parallel to the ground. This measurement determines your waist size. IMPORTANT: Do not rely on your jean size measurements. Just because your jean size is 34 does not mean your waist is 34 inches. Usually, your waist measurements are greater than your jean size.