  We show that the largely debated Planck-Einstein and Ott-Arzelies
relativistic transformations of temperature do not satisfy the closure group
property that two successive temperature transformations must be equivalent to
a single temperature transformation of the same form with the involved
reference frame velocities satisfying the velocity addition law of special
relativity. We then suggest relativistic transformations of temperature that do
satisfy this closure requirement and argue that they may be interpreted as
particular cases of the so-called directional temperature.
