A note on the relativistic temperature

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.