Butter

We have the expression “like a hot knife through butter” but in that equation isn’t the temperature of the butter just as, if not more important, than that of the knife? I mean say the butter is frozen. Hot knife, you’re still going to have to put in some effort. On the other hand, if you had melted butter, the temperature of the knife is kind of meaningless isn’t it? I’m not saying scrap the phrase, I’m just saying it deserves a little more specificity.