[@potatochipgolem]

Actually, funny thing about frostbite is, is that quickly thawing a limb affected by frostbite results in severely extreme pain and guarantees that flesh will be burned off, especially if it's a fireball thawing you out.

I'd imagine it's much the same with a burn victim and extreme cold.

If you'd like, you can do an at home experiment to experience a mild effect of it first hand. Just simply wash your hand in hot water, then quickly submerge in cold water right afterwards, or vice versa.