Weather could be a factor, but as far as I'm concerned, September is a great time to visit Galicia. The first time I visited Galicia was in September of 1988, and I remember that, especially in Santiago de Compostela, the fall crisp air, together with the occasional "llovizna" [misting rain] added something mystical to the ambience.
If you're into a little warmer weather, and that's your only criteria, you would better be served by visiting Valencia. We're not talking toasty hot, but certainly a little more temperate than Galicia.
I vote for Galicia...