I traveled across that part of Spain in 2016, but in small segments and often by bus rather than by train, so I cannot say for sure, but I'd be surprised if an InterCity train was not air conditioned.
Much of the area you'll be crossing could be coolish and overcast; it was for me. Leon was definitely quite warm, much more so than Vitoria-Gasteiz, Burgos and Oviedo. Santiago de Compostela itself is sort of notorious for not getting much sun. Still, a 10-hour train trip would be a risk in the summer without a/c.
What are you seeing on RailEurope that suggests no a/c? I do not ever use that website because it often doesn't list all the trains and frequently charges fares substantially higher than Renfe's.
There is much to see in the expanse between San Sebastian and Santiago de Compostela. If I didn't have time to stop in any of the places along the way, I'd definitely consider flying.