shortish water should be hottish water (damned autocorrect). Boiling water will soften the plastic too much on the 2 liter bottle and may allow the lid to pop off at a bad time (ask me how I know). Water hotter than I want to put my hand in is ok. (Yes, I know, real precise, but that's all I have).
Where is your cabin, what's the climate where you are living now. If it's Louisiana you have dramatically different concerns than if you're in central Alaska or Arizona.
Natural insulators tend to be flammable (wool is pretty resistant, but most of us won't find enough of that laying around). Examine your heat sources and examine how water can get into your wall and if it will be able to dry out. The other alternative is slip coated straw, which is also pretty resistant to flame from what I've read.
If the climate is normally pretty dry, straw can be fair insulation (yes, I realize it's flammable, so is your wooden wall). When I was a kid in Germany we lived in an old house with straw insulation and plaster on the inside and outside. In Alaska they sometimes used moss that they collected and dried. The russians have used peat (although it will hold 8 times more water than cotton, so think that through). If the thrift stores have lots of old, worn out blankets, that could work if you cut it into strips and stuffed it. Even paper or cardboard torn up small will work. Once again, all these things are flammable.
An earth or lime plaster on your inner wall would be a good idea. Make sure to push it into the cracks to help the plaster grip. If air exchange is a concern, make an opening that you can control to allow greater or lesser air flow.
If the cold is only an occasional, intermittant thing (like in Louisiana), maybe some wall hangings would help, maybe quilted. I know they used them in castles as a little bit of insulation and to stop the air leaks. (They looked cool also).
I'm not sure what is best if the climate is humid and warm. I'll let someone else jump on that grenade.