For light weight wool, generally it’s cooler. Look for 120gm fabric in a knit.
Since these can be less durable (snag easily and develop holes,) the usual practice today is to use some sort of polyester core for strength. Anything less than 140gm is good for hot weather, though. It usually doesn’t require special handling (washing) but it should be hung to dry.
It is a bit strange, but when you first put it on dry, it feels slightly warm. Often people will remove it saying it is too warm. But, after 10 minutes of an activity (hiking,) it will soak and distribute sweat over large areas of your torso. As it evaporates, it cools you better than most other fabrics, especially for runners. The knit also allows a high breathability, again cooling you. While you may get it salt stained, it is a better choice for warm weather. An occasional dip in a stream will also let it cool you for about a half hour or longer, depending on humidity.
Anyway, 120gm 100% merino wool tends to be very fragile. As was said, it may be far less durable. I put my thumb through one set pulling it over my head when wet. I believe Patagonia makes blended threads, with a polyester core, that gives the SUL fabric some strength. But, the addition of the plastics adds weight (~5oz for a shirt.) They make a limited selection of 120gm shirts with blended fibers (2 styles: short and long sleeved.) You might need some warmth, this is accomplished simply by wearing a second layer over them. This will close off the knit pores making them insulate, much like a mesh shirt. I believe Smartwool’s PhD shirts do this, but use a 140gm fabric. Ibex no longer makes a 120gm fabric shirt, but I had a couple that worked excellently for 3-4 years.
Wool does not dry really fast due to it absorbing some water directly into the threads. For drying, thin always dries fast, but a light weight plastic will dry quicker. Thin poly cloths tend to not have high breathablity, though. Icebreaker also makes a 120gm shirt but use a nylon core for strength, I haven’t tried that one yet.
Note that thin knits are NOT bug proof. Ha, ha…Do not buy blue. In summer, many bugs prefer blue/violet and UV colors, so, stick to plain white or light grey. Deerfly’s especially are drawn to blue.
Let’s see: Stretchy, yes;. naturally anti-bacterial, yes; dries quick-no; not itchy-yes.