Silk as far as textile fabrics go, is pretty warm for the weight. It has a combo of interesting properties that combine to make it so.
1. the fibers often are very fine–finer fibers trap more air than coarser/larger fibers.
2. the fibers are triangular shaped. A research study on fiber insulation and properties in garment form found that triangular shaped fibers trapped/stilled more air than round fibers.
3. It's made out of protein, and so it's thermally fairly non conductive, like wool and other protein based fibers, though it's different in some ways. So like wool, polyester, and polypropylene it has some "warmth" when wet properties relatively speaking–especially as compared to the more conductive materials like cotton, linen, rayon, etc and even nylon to a lesser extent.
But it has some down sides too. I've been looking for polyester-silk or silk-polyester blends to try out as baselayers. For some reason, extremely hard to find. Dri Release makes a Dri Release silk version, but that only has 12% silk. I'm looking for a higher percentage of silk to decrease odor and increase insulation. Would like to try around half and half, or 40% silk to 60% polyester or somewhere in between the former two.
It seems to me that a blend between silk and polyester would make a great baselayer. While it won't have the super excellent odor inhibiting properties of high wool to synthetic blends, it will be much more durable and possibly even a bit warmer, as well as dry a bit faster. Wool absorbs more moisture than does silk.
I've tried pure silk, its ok for sleeping and rest, but not so good for exertion. Some say silk "smells". I suspect that they tried the DWR treated silks, which of course will tend to smell more–the DWR treatment temporarily turns it more like into synthetic for that property. Untreated silk has ok to decent odor inhibiting properties. Better than cotton, much better than untreated synthetics (especially polypropylene and polyester), but not as good as wool or linen/hemp.
I'm a bit of fabric textile nerd…