Keep in mind that warm and natural/white are cottons. Cotton vs poly is a bit of a trade-off in some ways. Poly is technically warmer because as a synthetic, it doesn't breathe. All body heat remains trapped under the blanket. But that means it can be too hot in the warmer months. Cotton on the other hand breathes-which means it's never as hot and it probably wouldn't be as warm as your current blanket with poly batting (polar fleece is also poly). The warm & x battings are needle punched cottons and thus pretty dense, which definitely increases their warmth. But a denser poly would still hold more heat. All my warmest quilts contain poly batting.
You might also want to consider wool or wool blend batting. It has the advantage like cotton of being natural and is designed to be insulating (that is, to the sheep). This makes it warmer than cotton and more comfortable than poly. It's not exactly common in North America and it makes for a pretty heavy quilt. And you have to be careful not to get cheap scratchy crap. But the quality stuff is definitely an option, though an unusual one.