Top tip: Wool.
I started in late August, in a heatwave, and packed mostly man made tech fibre clothing, but had long johns and long sleeved top in merino wool. By the end of Sept (hello, Galicia!) I was wearing ... everything. Wool under my walking trousers, wool under my shirt and jacket. Bring wool. It is warm even when damp, doesn't feel too warm in the sun and doesn't stink even if you have to go a few days without washing and drying it, which is a bonus. In September (and in Galicia) you can't rely on drying weather every day.
Same goes for your socks - wool is a much better material for feet stuck in boots than man made fibres (in my opinion). Rub your feet with vaseline (or some used VapoRub), then put on thin liner sock and finally a good thinnish wool sock. Practically guaranteed to keep your tootsies blister free, warm and snug - but not overcooked, which makes you just as uncomfortable as being cold.
I also started with just a silk liner, thinking that plus the wool would be enough, but it wasn't. Not for me, anyway. I ended up buying a thin summer sleeping bag which compressed to an incredibly small size, and with the silk liner inside and my woollies on, it was fine. Some of the old, stone buildings can get pretty cold at night!
Also it was a lot windier than I had expected. Bring a sun hat if you want - I gave up on mine because it always blew off! - but take a wool or fleece hat too, to keep your ears cosy.
Next time I go, which will probably be around the same time, I am taking merino T-shirts, my wool ensamble from last time, and an extra fleece.
I also could not have done without my
Altus rain jacket/poncho, there are lots of threads on it in the forum.
Happy planning and buen camino!
Linda