Here is an article that quantifies the heat loss effects of cotton, polyester and polypropylene: Rossi et al., Dry and Wet Heat Transfer Through Clothing Dependent on the Clothing Properties Under Cold Conditions, International Journal of Occupational Safety and Ergonomics (JOSE) 2008, Vol. 14, No. 1, 69–76.
Experimental Summary
Here is a rough summary of their experimental setup so you can understand the applicability and limitations to real-life scenarios.
- Test on a human manikin which simulates body heating and sweating.
- The clothing was fit similarly between materials as much as possible and consisted of underwear covering upper body and legs
- Clothing consisted of an inner layer (cotton, polyester, or polypropylene) and an outer layer (categorized by being impermeable, semi-permeable, and permeable to moisture). This two-layer system more accurately simulates real life layering. (You probably aren't just going out in the cold in a t-shirt). Here is the information on the materials:


- The amount of sweat produced by the manikin is kept constant for all trials (550 g)
- The length of time per trial is 2.5 hrs, under steady-state conditions, with an ambient temperature of 10 C.
- Not specifically stated, but I believe overall heat loss rates are measured by the manikin (how much heat required to keep the manikin at a certain temperature).
Results
Moisture Distribution in Layers
The change in mass of each layer was measured after the experiment to determine how much moisture was absorbed. Cotton contains almost 4x the amount of water as polypropylene (a much more hydrophobic material). Also note that more of the water is contained right at the skin layer for polypropylene and polyester.
The outer layer makes the biggest difference in where the moisture goes, with semi-permeable and permeable outer layers resulting in most of the water being evaporated.
This tells us what we already expect, but how does that effect total heat loss?

Effect of Wet Conduction
Much of the argument against cotton is that when it's wet, it transfers a lot of heat from your body. While this is true if all you are wearing is a single cotton layer, it doesn't seem to hold up when you are wearing an outer layer. When comparing the heat loss of cotton + impermeable outer layer with and without sweating, the authors state:
The additional heat loss due to wet conduction at ta = 10 °C was calculated to be only 0.9 W/m2, which accounts for less than 2% of the additional heat loss observed. [...] For impermeable clothing combinations, wet conduction can only explain a small fraction of the additional heat loss seen.
The main reason this occurs is that the total thermal resistance of an outfit is the sum of thermal resistances of the layers. Thus, even if you have a really thermally conductive, water-soaked layer, heat is still limited by the most thermally insulating layers.
Evaporative Heat Losses
The figure below shows the evaporative heat losses for different materials combinations. Because cotton retains more water, less water evaporates, resulting in lower heat losses.

Heat Loss of Permeable vs Impermeable Outer Layers
The following figure shows heat loss results for different outer layers while keeping the inner layer polypropylene. Notably, total heat loss is lower for an impermeable outer layer compared to a permeable one. The reason is that evaporation of water is higher (see the previous figure), which removes energy from the body.
Despite an impermeable layer having higher liquid water content, total heat loss is lower due to less moisture evaporation.

Conclusions
While cotton does retain much more moisture than other synthetic materials, it does not necessarily translate into significantly larger heat losses when layered with an outer shell. Breathable and water wicking layers will remove water, but at the expense of evaporative heating losses. The comfort of not having a moist layer next to your skin is another issue to consider, though.