Yes, that's the right idea (assuming it has lower entropy when it's frozen than when it's liquid). In the context of the liquid you describe, and assuming it has otherwise normal properties then yes you can't warm it up (= add energy) and make it positive again. And if you took it outside, the temperature would first become more and more negative and then flip to positive. However, as long as we are talking about exotic stuff it is conceivable that as you add energy, the entropy first decreases (i.e. negative temperature) but if you add more and more energy, the entropy starts to go up again. For example lets say that if you add a lot of energy to the frozen stuff, it becomes a gas. I'm not sure if a system like that where you go from positive to negative to positive is physically possible, but I don't currently see any reason why it wouldn't be.