When you visit a sauna, the common advice is to take two towels: One to sit on in the sauna, and another to use when you dry off. The January 2013 Journal of Craniofacial Surgery makes this explicit to the medical community in a paper describing the conductive contact burn.
In the paper, they describe a trip a 70-year old woman made to a Korean Sauna. During her visit, she went into a hot dry sauna room, covered her thighs with a wet towel, and fell asleep for 30 minutes. When she woke, she found her thigh burned, and covered with large blisters: a classic second-degree burn. Because of her age and other medical conditions, she was hospitalized for two weeks after the incident.
If you have ever attempted to remove a hot pan from an oven using a wet towel or potholder, you have experienced this situation: Wet fabric conducts heat much more quickly than dry fabric.
Fabric insulates by trapping air inside the gaps in inside the weave of the fabric. A towel is an especially good insulator because it is woven to have lots of gaps. Air is a very poor conductor of heat.
Those same gaps in the towel serve another purpose when exposed to water: They absorb water, which is a very good conductor of heat. A damp towel will transfer heat more quickly than a dry towel, while a completely sodden towel will transfer heat almost immediately.
This is more critical in certain Korean saunas, where temperatures can approach 400°F (200°C), than in a Finnish sauna, where the temperatures are rarely above 230°F (110°C). Many of these saunas recommend that the patrons cover most of their exposed flesh with cotton or burlap blankets to minimize discomfort.
So remember, when you visit the sauna, take two towels, and keep the one you’re using in the sauna dry.