You guys lack fortitude. 13oz linen is pretty light. 15oz+ is better; Mersolair has some which are 500gm.I don't believe anybody who says 13+ oz linens wears cool. It doesn't, unless you run ice box cold to begin with.
God forbid humidity enters the mix.
Thermodynamics are such that a porous tropical wool will not help you if it's 100 degrees. All you're doing is letting more hot air in. In that scenario some kind of loose-fitting heavy wool is probably best, such as what Obi-Wan Kenobi wore on Tatooine.