Is it OK to melt the butter in the scalded milk?

Hello,

I would appreciate some advice on a sweet dough recipe I make. Since the recipe uses whole milk, I like to scald it and cool it before mixing with the flour. Many days I also seem to forget to get my butter out to come to room temp.

Over the last several times I've made the dough, I have been adding the cold butter right from the fridge into the hot milk to cool the milk fast.

I can't really say that I have seen a decline in the quality of my product, but was wondering what those with more experience might think.

Thanks