At the point where the air hits 1400 Fahrenheit, I'm gonna say the situation is comparable to total immersion, which deals 10x damage. But okay- even if you were only looking at 1d6/round, how many rounds does it take to check all the rooms in a four-storey building, or start failing suffocation checks? The latter in particular is save-or-die.
To address Kish's point: If Miko genuinely believed she was in no danger, then yes, it would still be a distinctly good thing to do, consequentially speaking, but as a measurement of her commitment to principle it would be lot more tepid (all she'd be sacrificing is spare time.) But I think it's implausible that she'd get to the second or third floor without noticing, e.g, all the blistering heat, dense smoke and falling timbers.
I'll fully admit that having buckets of hit dice and good saves would greatly improve Miko's odds of survival, but this is still one of the few environmental threats that can genuinely kill high-level D&D characters. (Also of note- if your corpse is cremated, nothing beside True Resurrection brings you back.)