I get that rash on my hands and arms if I visit hot or sunny climates, or in the beginning of summer here when I am out in the sun for the first time. Sun screen doesn’t prevent it either. I make a point of wearing long sleeves and gloves when riding in the sun. I find the kind of shirts designed for sports like hiking, mountain climbing, etc are very light weight and not at all hot - the breeze goes right through them, but the sun stays out. Brands like Arcteryx, and choices from REI or EMS are often useful. They are made for moving, so although they are usually fitted (not baggy), they are cut to allow good range of motion and comfort, and don’t ride up around the waist, etc. Shirts for yoga, often made of cotton, can also be nice, as they are usually fitted but not tight, and they are stretchy and light weight.