my first try and i was wrong...
i thought it was a person who is very hungry...why? because if you're really hungry and you're eating something...you'll swallow it even before the butter melts.hehehe
It is believed that this saying originated because butter melts in a warm environment. A person who is guilty but playing innocent is considered cool or even cold and calculating. So cold that butter wouldn't melt in his mouth.
Very good explanation.I heard this idiom first.With this explanation I learned the reason why it is said so. I thought 'guilty'.