Butter wouldn't melt in his mouth
Prim and proper, with a cool demeanor
The allusion in this expression is to people who maintain such a cool demeanor that they don't even have the warmth to melt butter. This is an old phrase - here's a citation from 1530, in Jehan Palsgrave's Lesclarcissement de la langue françoyse:
"He maketh as thoughe butter wolde nat melte in his mouthe."
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."