Bunker gear has a vapor liner and insulation, and routinely get wet. Most artificial fabric has a low melting point, and it tends to turn into burning goo that melts into your flesh.

But wool, silk or even cotton is surprisingly thermally resistant, at least for very short exposures. Water reduces that resistance and wetted out fabric transports thermal energy through the fabric faster and more efficiently than the dry fabric fibers and the air pockets between them do. The moisture can convert to steam, as well. Wet fabrics are slower to ignite for precisely these reasons.

There is a simple experiment you can do. Take two identical fabric samples and wet one of them. Place them in a very hot dryer or under a very hot iron for an equal length of time, then drape each one over opposite forearms. While not a perfect model, it will adequately convey the idea.