They are wet.
Not just wet, but furry and wet. Water has a high specific heat
The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C
which is higher than any other common substance. As a result, water
plays a very important role in temperature regulation. The specific
heat per gram for water is much higher than that for a metal, as
described in the water-metal example.
So: water will absorb heat and heat up slowly, giving you the degree of fire resistance you want. The best way I can think of to have a lot of water on body surfaces is to have it held there by fine fur, or maybe matted fur like my cat. If the water is salty too it will evaporate less easily, although the specific heat is slightly less. Your creatures will be furry like a cat but sweat like a horse. Or a human. Except humans don't have hair on their palms unless... anyway, most humans don't.
If you don't want them wet all the time and don't want furry hands, you could have them sweat like mad in the presence of heat. Which I certainly do. Also if I am in a high place (or even think about it) my hands sweat. For better grip? Anyway, your creatures could pour sweat out of any body part in the fire. That would work well. It might be a little hard to explain in prose - harder than saying they are are covered in soaking wet fur clumps.
Maybe you don't want your creatures to be wet all the time and you don't like the sweat on demand idea. Instead, you could have them be oily. Some furry things are oily, especially aquatic mammals, and the oil stays on the fur. Olive oil (as an example of an oil) has a specific heat about half that of water, which is not bad.
It could serve the same function. A problem with oil on the fur is that if it did get hot enough to catch fire, these poor creatures would really burn hot and the fire would spread over them fast.