Monica it can vary a lot from year to year.
I walked on the CF in June 2008, and in Estella I decided to post home my good wind jacket, as I thought it would be warm now that I was in Spain and it was summer. But as it happened, quite a few times I wished I still had that jacket with me, as there were some bitterly cold days, with a freezing wind. It never consistently warmed up until I had walked across most of the Meseta, and was approaching Leon. I have since learned that summer in 2008 was the coldest for ten years. But I have friends who walked on the CF in June 2009, and it was warm for them nearly the whole way....
I don't like walking in too much heat either, so mostly I started early when I thought it was likely to be a hot day, and I walked for about 6 hours but never walked much past lunchtime. I decided some days to stop after 20km rather than pushing on another 7-8km to the next village in the heat...
Margaret