Fun fact: even when using an absolute scale like Kelvin, it's theoretically possible to have a negative temperature!
The reason for this is that temperature measures how much energy you have to pay in order to increase the number of possible microscopic states accessible to the system by a certain amount. In really weird systems it is possible that the amount of energy you can put into the system has a cap, so if you keep pouring energy into the system then eventually it will be forced into the unique microscopic state where every part of the system contains as much energy as it possible can. When this happens, the only way to increase the number of microstates that the system can be in is by removing some of the energy from the system--which you can visualize as creating the possibility of there being holes in the system where there is an absence of energy--and so the temperature is negative.
This kind of system is so weird, though, that is existence is primarily theoretical. Last time I checked, such a system has not yet been demonstrated to exist in a lab. Still, it is fun to think about!