They have electricity though right? Then they’re not too rural to have AC?
But it's worth browsing pictures of the abbey to get a sense of how challenging this would be. https://www.comece.eu/christian-artworks-benedictine-archabb... Most books reside in giant, wall-flush bookcases with no natural ventilation. Establishing decent airflow -- without accidentally ruining structural walls or turning the bookcases into perforated messes -- seems very hard.
You do not need to run ducts, just piping for (say) mini-splits.
By the way, I was always curious why installing splits _in_ the room. I understand multi-story apartments, where there's no other place. But if we're talking about detached houses you have an attic (where the airducts go), or a ceiling (where recessed lights go). Can we put splits in there? I can see problems with power delivery, condensate diversion, but they are the same if we install them _in_ the room. But in return you get fine-tuned climate control, and no pressure difference problems (no need for bypasses to prevent slamming doors with ducts).