Warm and Natural has a polyester scrim - so it is not 100% cotton. One of those "read the fine print" things.
I purchased a roll of Warm and Natural many years ago - and when I soaked it (in hot water - gasp!!), it turned the water very yellow. It may be different now. Anyway, I would hesitate to use that on/in something that was very white.
The Warm and Natural survived the soaking very well - in fact, I had one piece I had to wash twice - one of my cats "anointed" it - and it turned out fine.
However, I do not agitate the stuff - only soak, rinse, spin - and then dry it on "medium" until "dry" - but not "cooked"