Your creatures will smell like burnt stuff.
Merely trying to remove stuff from your skin mechanically will not do, there will always be some leftover. It is also not practical to remove sweat.
Speaking of which, sweat isn't just pure water (otherwise it wouldn't smell!). It's water plus bodily wastes and some more things. The wiki lists:
- Lactic acid
- Many different minerals
And then it says:
Some exogenous organic compounds make their way into sweat as exemplified by an unidentified odiferous "maple syrup" scented compound in several of the species in the mushroom genus Lactarius.
Don't forget it's loaded with bacteria, which will produce their own stuff.
Why does it matter? Because while water will simply evaporate over 100 degrees C, other components will break down into other stuff - urea will break into cyanuric acid, ammonium chloride and ammonia, so during a fire bath a creature will be very hard to approach even for other creatures resistant to fire.
After the bath, the minerals will still be there, dried up. A lot of salt will remain, for example. It's melting point is at 801 Celsius. So you have very hot salt, which will trap a lot of material from the bacteria, might give you a burning smell.
Then there is also some sugar in sweat. It will break down into carbon chains. Whatever doesn't evaporate will recompose as some either brownish or black tar. That's the kind of thing that makes unwashed teflon pans sticky. Consider the effect of this for your burning creature.