No. Absolute zero is the temperature at which the kinetic energy of atoms/molecules/subatomic particles/anything else has gone to zero. Having something be at a temperature less than absolute zero would imply that the kinetic energy of the particles involved was negative, which requires either negative mass or imaginary velocity (if you have both negative mass and imaginary velocity, your kinetic energy is real and positive, but your momentum is imaginary). Going backwards merely implies negative velocity, which still gives a positive kinetic energy if we assume positive mass; since nothing known has negative mass, this implies a positive nonzero temperature as measured in the Kelvin or Rankine scales.

First off, I was kidding...it was a reference to a Doctor Who episode that had a "Cold Star" that gave off cold...

And second off...

They start going backwards...

I was *again* kidding....I'm fully aware of the physics involved...

Third, temperature is technically not defined based off of kinetic energy...that actually would be a terrible definition since kinetic energy is 100% relative....temperature actually is the inverse of a more important physical quantity, the (thermodynamic) beta value...the beta value represents the relationship between changes in energy and changes in entropy (it's proportional to the partial derivative dS/dE -- I don't remember which things are held constant but probably volume and/or number of particles since I know those affect entropy)...

Finally, temperature, given the more rigid definition above, actually can be negative if you have a system where increasing energy actually decreases entropy...there are few pathologies in quantum physics where adding energy decreases entropy...certainly not relevant to most systems but it is doable and definitely does not require negative mass....