Reheat your drink as needed, you don't want to butter to get too cold...it will start to separate from the drink, which is gross!
Feel free to mix up a big pot of this, but I like to add the butter and rum to each serving (a little OCD here), just keep it hot on the stove top and give it a good stir before serving.
Use high quality unsalted butter. I use and love Kerrygold.