When I last walked in October 2018, temperatures were high (30+) at the beginning, ameliorating as the month went on and I went north. I can certainly imagine the possibilities of hot weather in September.
But last year I walked on the
Camino Frances between Sahagun and Leon when temperatures reached well into the 30s and it never was above 24 when I was walking. I just started early and had my walking done by mid-day. The hottest part of the day is, after all, in the later afternoon.
I should also point out that the Spiritual Variant isn't south of Galicia, it is completely within Galicia. And last summer, when there was a huge heat wave across Spain, it didn't reach Galicia. There is no predicting the weather.
I always say that the best time to walk a Camino is when you have the time available. If you have the time in September, I wouldn't worry about it too much.