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The novel hydrodynamic model of plasmas with the relativistic temperaturesconsisted of four equations for the material fields: the concentration and thevelocity field \emph{and} the average reverse relativistic $\gamma$ functor andthe flux of the reverse relativistic $\gamma$ functor is applied to studyhigh-frequency part of spectrum of electromagnetic waves propagatingperpendicular to the external magnetic field. The thermal effects consideredfor the temperatures close to the rest energy of electrons considerably changethe dispersion equation in compare with the nonrelativistic temperatures.Analytical analysis of the changes is presented.

On a hydrodynamic description of waves propagating perpendicular to the magnetic field in relativistically hot plasmas