We're starting off with a Japanese mythical creature, the Yuki-Onna. Now the specifics of this being vary quite a bit from one tale to another, so let me be specific what this being is about. Keep in mind that this is my version, and may therefore deviate from popularly held versions.
Yuki-onna are ghosts of women who died during snowstorms. They're beings that begin being corporeal but can learn to 'phase through' other things (temporarily becoming incorporeal). They are essentially frozen corpses, so their core temperatures are well below -50 degrees Centigrade. Their lungs are filled with air of that same temperature, so they don't have 'ice breath', they just cool the air as they breathe out. Their diets and circadian rhythm is unimportant for this question, so I'll skip that.
What I want to know is: how are they affected by a fireball type spell? Say they breathe in the flames, does the temperature of the fireball affect whether they 'melt'?
The problem I am having is this. Ice (frozen water particles) should melt in layers, which would then need even more energy (heat) to vaporize. So, in theory, Fire shouldn't be 'super effective' against ice. It would take too long to be effective.
So, if I hazard a guess, I would say that there would be a insulating layer of ice on the skin of the Yuki-Onna. The flames would first have to get through this layer (via the same ineffective methods of heat transference), before melting and burning through skin, then blood, internal organs, etc.
Would fire therefore be the most effective method to combat beings of this nature? Or would the airways allow for the heat to circulate into the core and heat up quicker?