Yes, you absolutely can go negative in temperament. Higher means more submissive, lower means more dominant. Zero is essentially the boarder between the two.
Frequently, especially early on, there are points where you have two yellow options. One of them will net you a positive temperament stat, while the other will net you negative. The best example I can think of off the top of my head is really early when the guards catch you peeking on Sage and the prince in the bath. You have an option to be meek, or to slap the guard. Either choice impacts the stat, one plus and one minus. Pretty obvious which is which.
It's important to note that slutty and temperament are not necessarily related. On my personal preferred play-through, I wind up with a temperament stat in the area of around -15 or so and a sluttyness stat well over 40. Boring, it is not.