Relativistic transformation of temperature

We reconsider the long standing problem of the transformation of temperature in special relativity. Using the radiation field as a working system, we show that there is no unique law of transformation. Indeed, the moving system appears hotter than the system at rest. This transformation law clearly depends on the thermodynamic quantity under study. Contrary to temperature, pressure can be Lorentz invariant, depending on the axis of observation. Moreover, entropy, photon number, and sound speed are Lorentz invariant. This is the principal result of this work.