In the photograph, Peter Harvey's fresco jacket is combined with a shirt of Carlo Riva Lino Arsenal, a Simonnot-Godard pocket square and a Drake's London bow tie. Perhaps the least appreciated of those is the linen shirt, which is another of that set of things that deserve to be more common than they are.
Until the rise of cotton, linen was the most common fabric used close to the skin, which explains the name linens for shirts, handkerchiefs and bedding even though few of those are commonly made from linen any longer. Labor intensive to produce, the economics of linen usually require a higher price than cotton and the cost limits its popularity. On the other hand, linen wears cooler and absorbs moisture better than cotton, making the stuff a particularly comfortable choice for hot weather.
A second negative to linen besides price has been that in shirting weights the stuff creases when it is so much as looked at. Pure linen shirts are one of those things that should be changed at least once a day, which is hardly practical for men who need to be out and about for most of the time. And that is where another one of those blended fabric miracles of modern weaving technology comes into play, for Carlo Riva and David & John Anderson, the two best shirting makers of the world, each offer 50-50ish linen and cotton blends with a finer hand and a reduced propensity to crease than pure linen. Better still, in the somewhat rarified air in which these fabrics play their price is no more than the best pure cottons.
The usual knock on summer shirtings is that they can be sheer. Neither Lino Arsenal or DJAs Zephir 170 have this trait and that makes them perhaps the best choice for hot weather dress shirts.