Why does the cool feeling of silk fade after your skin rests on the same spot for a while?

Answer: The contact patch warms up to skin temperature

The contact patch warms up to skin temperature ✓ — Correct! Silk feels cool because it conducts heat away from your skin quickly at first. Once that patch has warmed to roughly your own temperature, there is no longer a temperature gap to drive heat out of you, so the coolness disappears. Move to a fresh patch and the sensation returns instantly, which is why people shift position on silk sheets.

The silk runs out of its stored coolness — Fabrics do not store coolness like a battery. What you feel is a flow of heat out of your skin, not a supply of cold flowing in. A cool-feeling material simply moves your body heat away faster than air does.

The surface texture changes as it is pressed — Pressure can flatten a weave slightly, but texture is not what you are sensing here. The disappearing chill tracks temperature, not smoothness: a silk sheet feels exactly as smooth after ten minutes, yet no longer feels cold.