How do you build from casual conversation to spicier stuff?

I'm writing a fic shipping two characters who are very familiar with each other on a professional level, but don't interact much at all on a personal level. Both characters are quite stoic and reserved (and, for extra challenge, one is the President of the United States...), so I'm finding it challenging to smoothly bridge the gap from "Great work." to "Let's please make out!" in a sensible way. Any advice is appreciated!