that sucks, because I don't like wearing my puffy and beanie to bed!
Welcome to the Camino! This is one of those times, when we veterans just say: It is what it is.
Pilgrims have been walking these routes for more than a thousand years, with much less protective clothing than we enjoy today. Perhaps they were made of sterner stuff. Or perhaps this is part of the reason they had short lifespans - whatever!
In my experience, in many places, they will turn on the heat for perhaps one-hour at about 0500 - 0600. If you can ask "if and what time" your particular place of accommodation does this, you can plan accordingly. Try to be thoughtful of your fellow pilgrims.
Other than that, the optimum sleeping solution is to put on the clothes you plan to wear the next day, after you bathe. Wear your fleece layer, and or a puffy if you have it. Also, keeping your head, hands and feet warm is essential to not losing too much body heat.
I always recommend a close-fitting beanie hat, wool socks - the pair you planned to wear as an outer layer in the morning, and a pair of gloves - any gloves. Absent having gloves, an extra pair of socks makes a good field-expedient pair of mittens.
Finally, anyone who starts a Camino in October should carry a proper sleeping bag, or warm down sleeping quilt. DO not rely on the place of accommodation providing a blanket, or at least a blanket you would want to use.
The key concept is to be self-reliant.
Hope this helps.
Tom