Cotton is a great menswear material that absorbs heat if it’s woven right. It’s lightweight and breathable and is by far the easiest to wash and dry without special care. However, tight weaves of cotton hold hot air close to the body, and sweat or water evaporates from it very slowly.
Seersucker is one of the lightest cotton weaves, with a dimpled surface that lets air flow. It’s a joy to wear in the summer and one of the best options available.
Madras (true Madras cloth, not just the reddish plaid print) has a very loose weave that lets air flow and dries quickly. There’s very little domestic production in the United States, so it can be costly unless you happen to be in India.
Gauze is more commonly associated with medical bandages, but the large weave with its visible square gaps was used for tropical military uniforms for some time and is reappearing in consumer clothes as well. It’s another good option, though not as durable as Madras or seersucker.
Drill or twill are both tighter weaves that hold in more air and moisture. Unfortunately, they’re also cheap and common, and make up the majority of most commercial lines. Wear them when you need a bit more durability but aren’t expecting to exert yourself too much.