I have often heard that wet cotton is an extremely poor insulator of body heat, variously compared against wool and being naked. I would like to see this tested, for I am skeptical.
Start with cotton and wool swatches of identical dry insulation rating. Moisten the swatches with identical amounts of water, or in a separate experiment, moisten them to saturation.
Heat transfer may occur through three mechanisms: diffusion and convection(?), and evaporation.
In diffusion, vibrating molecules induce neighboring vibrating molecules to vibrate. The heat transfer of diffusion of the wet fabric is probably a linear combination of the heat transfer of diffusion of the dry fabric, defined to be the same by initial choice of fabric, and of the water. With identical amounts of water, this factor will also be the same. Moistened to saturation, it will depend on the maximum amount of water the fabric can absorb.
Convection (that's probably not the right word) will occur if the water moves, transporting heat with itself. The fibers in fabric will probably slow water motion a lot to the point where convection is negligible. Convection does occur if you are being rained upon and you are naked, the rain rolls off your skin, carrying heat away. This is why I am skeptical of the statement that wearing cotton is a worse insulator than being naked when being actively rained upon.
Upon further consideration, convection does occur by capillary action from wet to dry. However if you are being rained upon, the water would be traveling in the wrong direction to carry heat away from your body. (It is good if you are sweating. )
I don't have a good feel for capillary action. It probably depends on the gradient of moistness between the outer and inner surfaces of the fabric, so is not relevant if the fabric is fully saturated with water. It also probably depends on fiber thickness, and density.
Evaporation can carry away heat. But in a situation in which you have just been rained on, or are currently being rained on, and you are trying to stay warm, the humidity is probably very high and the temperature low, so very little evaporation should occur.
The evaporation rate of a fabric depends on fiber surface area.
My reasoning can be refuted by experiment. I am curious where my reasoning is wrong. The experiment has probably already been carried out: if wet cotton's poor insulation were a myth perpetuated by the wool and synthetic fabric industries, the big cotton industry would probably not stand idly by losing profits to such a myth.