Origin of "Butter wouldn't melt in his/her mouth."
Solution 1:
The Phrase Finder has a citation from 1530, in Jehan Palsgrave's Lesclarcissement de la langue françoyse:
He maketh as thoughe butter wolde nat melte in his mouthe.
It goes on to say,
The phrase is usually used in a derogatory and critical sense and, in the past at least, was most often applied to women. Occasionally, it was used to denote a quiet meekness and sweetness of temper rather than emotional coldness. For example, this description of Mr Pecksniff in Charles Dickens' Martin Chuzzlewit:
It would be no description of Mr Pecksniff's gentleness of manner to adopt the common parlance, and say that he looked at this moment as if butter wouldn't melt in his mouth. He rather looked as if any quantity of butter might have been made out of him, by churning the milk of human kindness, as it spouted upwards from his heart.
Solution 2:
Eric Partridge offers this citation in A Dictionary of Slang and Unconventional English:
butter would not melt in one's mouth, (look) as if (To seem) demure. Coll. from the 1530's; Palsgrave (O.E.D.), Latimer, Sedley, Swift, Scott, Thackeray. In reference to women, Swift and Grose add: yet, I warrant you, cheese would not choke her, the meaning of which must be left to the reader who will look at cheese.
So, onward to cheese, we find — nothing useful. Partridge is curiously silent on the subject, at least as it relates to this case directly. I wonder if his reticence might be due to one unsavory meaning of the word, use of cheese for smegma, giving the whole thing a lewd sexual connotation. But I can find nothing in the O.E.D. or elsewhere to support this contention. Still, if cheese is somehow related to butter in this context, this could well shed a whole new light on that phrase as well. But given the lack of sources, I have to conclude this is a dead end.
Still, we might also consider another meaning of butter as "fulsome flattery, unctuous praise" (Partridge). A young woman who was demure, as Partridge calls it, would be likely to receive much of this kind of butter.
demure |diˈmyoŏr| adjective ( -murer, -murest) (of a woman or her behavior) reserved, modest, and shy : a demure little wife who sits at home minding the house.
A woman who was "reserved, modest, and shy" would probably seem a little cold, and certainly resistant to the kind of buttering flattery that might come her way.
Solution 3:
I would offer the suggestion that butter and cheese though both dairy products have varying melting points. Though butter may go soft at room temperature (and some cheeses) I might infer that the suggestion from this quote may be that cheese would in fact melt in her mouth and therefore butter wouldn't stand a chance. The key to this being that she 'looks' as though butter wouldn't melt although the truth is that cheese would not choke her. Perhaps therefore it has 'melted' or at least gone soft. Good old hot lips.