Making a (first century AD) tunic

[Tarbicus]

Maybe I'd been somewhat diverted by the "modern" view of woolen clothing as now being almost entirely designed to keep you warm, while actually lighter wool products have only been replaced by cotton or other fabrics in our time.

A good and decent modern suit made of wool will keep you warmer in winter, and still be wearable in the summer. There's no reason to suppose Roman woolen fabric was any less so given the centuries of experience, with garments made in almost every home. IIRC, fragments have been found that outclass the finest modern gabardines (it's mentioned here on RAT somewhere).