This is a common question and a lot depends on your needs. When I did the
Camino Frances from SJPP to SdC in 2001 I did it during the month of July. I only took a flannel sleeping bag liner. I thought that it would be hot in Spain in the summer but in fact, as Spain is second only to Switzerland as the most mountainous country in Europe, I was frequently sleeping in places over a couple thousand feet above sea level (Leon, Astorga among others) and it gets quite chilly up there at that altitude.
What made matters worse was that during the summer it's so crowded. Beds go fast, and I can't even tell you how many times I slept on the floor, in a hallway, and once on a kitchen table. I really wished that I had had a warm down sleeping bag as I got quite chilly.
So, having said all that, I would very strongly recommend a lightweight down sleeping bag such as those sold by Marmot, Mountain Hardwear or Zpacks.com. Something in the neighborhood of 500 ro 650 grams. This way you'll be sure to have a warm and cozy night's sleep regardless of the chilly refuge with the open window or the monastery floor with that cold cement.
I would even recommend a lightweight inflatable mattress (about 300 grams) but that's another story.
Have a wonderful walk and stay warm and cozy!