Depending on what you deem “temperature”, that is actually possible :) The physical definition of temperature is the derivative of energy with respect to the entropy. With most physical systems, like gases, if you put in energy, the entropy increases. This happens because if the energy is not bounded from above, the amount of individual states the matter can take always just increases. So the temperature is positive. If the system has a maximum energy, as it can be constructed in some nanophysical systems, the number of reachable states may decrease towards the maximum. So, if you’re in this area, your system technically has negative temperature.