If you have 100% cotton garments you want to get more longevity out of, washing on cold water + letting them air dry is the way to go (although sticking stuff in the dryer for ~5 minutes on the lowest possible setting before putting it on a hanger is fine to help fluff out any wrinkles). This also goes for anything "nice" that you want to keep in the best possible shape, even if it's not 100% cotton--don't forget that dryer lint is partly the result of your clothes' fabric sloughing off, which is why some shirts get paper-thin if you own them long enough!

I wear a lot of 100% cotton (including 100% linen) shirts that still look and fit almost like new, since I'm a stickler about laundering them this way. Towels, on the other hand, get maximum heat for both washing and drying, and you can really see the difference. I use a lot of 100% cotton washcloths from those Target multipacks, and recently bought a set identical to one I'd bought a year or two prior; the new one was larger, a little softer, and a much brighter color. The old one had shrunk to a pale, slightly scratchy ghost of its former self!

On exactly one occasion, I accidentally threw a 100% cotton shirt in the towel hamper and didn't catch it before starting the load. It's not a shirt so much as a crop top now :)

Linen typically means flax fibers.