@JavelinJoe
Nope, but the author could have made a more plausible scenario.
E.g.: The setting for the night is not completely set for desert like temperature but something around 10 degree celcius instead of below 0 degree like a desert.
Then it would have still been cold enough for a human without proper clothing to freeze but high enough for the 2 of them to survive.
@TrueGoddessReincarnation
Yes, the transformation is part of the settings of the manga.
So that is acceptable.
But then the author should stick with ALL aspects of this transformation consistently.
And that is what he does not do here.