I walked twice from mid May to mid June on the Frances and this year in May on the Primitivo. I always bring a sleeping bag. There can be some cold nights and weather can be unpredictable. I keep telling the story of how it snowed at beginning of...
I brought a silk liner and a lightweight quilt that I used inside the liner. One night they put the heat on at the beginning of June, and other nights I slept in just underwear. You never know!
I did CF SJPdP to Finesterre in late May 2018 with just a silk liner. All but a couple of albergues had blankets, and where there were none I just slept in everything I had with me....including a cold night spent in a Foncebadon refugio's garden...
If you want to always be comfortable then you might want a sleeping bag, because you might have a few colder nights. But I would bring just the liner. If that's not enough, then look for extra albergue blankets. If they don't have any, start...
I have used my rain poncho as a cover over my silk liner bag in mid summer in Galicia as a cover. It can be chilly and I would not depend on or use seldom washed albergue blankets if available.
Don´t assume it won´t rain, so a rain jacket is a good idea. If it is cold, you can layer up underneath it. Most albergues provide blankets so a thermal liner should be OK if you really want to travel light but a light sleeping bag if you want to...
I bring a sleeping bag rated for 20⁰C, i.e. indoor sleeping. Not all albergues provide blankets. If too hot, I unzip it. You can probably get away without a jacket if you layer properly. I generally bring convertible pants, and long sleeved...
You could encounter some cool nights, so it depends on how hot or cold you sleep, if there are blankets in the albergue that you would be willing to use, or if you could just wear all of your clothing to sleep in.
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