The first Camino I walked was the French, and I took a sleeping bag, which I used most nights; however, like all sleeping bags, it took up a lot of space in the backpack. On all subsequent Caminos, I simply took a silk liner. The pack volume is very small, and in almost every Albergue, there are blankets available to keep you warm.
I say almost every Albergue, as twice on the Norte, I arrived at a municipal Albergue where there were simply the usual blue mattresses and pillows. When I asked about blankets, he simply shook his head and said "no blankets" (in Spanish obviously). At this point, I noticed everyone was getting out their various sleeping bags apart from one American fellow who was in the same boat as me -I pulled my best Oliver Hardy slow burn to camera expression!!
)
I then proceeded to put on all my clothes, two pairs of socks, my hat, and my jacket and put my feet into my backpack. I can't say I slept well, but I dozed enough hours to feel refreshed the next morning. Two days later, I passed a Decathlon store and went in to look at sleeping bags, then (and I assure you this isn't because I am Scottish) decided it wasn't worth buying a sleeping bag and continued with my liner. About a week later, I went to another Albergue again, which I will not name, but without a doubt, it is the worst one I have stayed in throughout my six Caminos. The owner of the place had a very bad attitude and a hugely over-inflated opinion of his Albergue (it was unclean, rundown, and a pale reflection of what it was 30 years ago). I asked about blankets, as it was wet and chilly, and he said "no blankets". When I went to do my laundry I opened the cupboard and there were plenty of woollen blankets, I took two without him knowing and replaced them the next morning without him seeing.
But I would say both of those occasions were exceptions, and upon reflection, I could've booked myself a private room in a hostel to get a more comfortable night's sleep.
My vote is go with the liner.