I know of " negative temperatures" as sometimes applied to spins and laser, but those are different thing from what I have in mind. As wikipedia says,
Such temperatures do not have the standard meaning of temperature, which is that heat flows from body with higher to body with lower temperature. When you connect such spin system with -5 K to 5 K system, the -5 K system has more energy and will give it to the system with 5 K. Such concept of temperature defines negative temperatures to conform to the laws of entropy.
But this is not without objection - such systems are not stable so it can be argued they do not have temperature at all.
I am thinking of a concept of temperature applied only to systems in equilibrium, with which, when a body has temperature -5 K, one says the body is truly colder than the system with 0 K, so heat will flow from 0 K to -5 K.