  The novel hydrodynamic model of plasmas with the relativistic temperatures
consisted of four equations for the material fields: the concentration and the
velocity field \emph{and} the average reverse relativistic $\gamma$ functor and
the flux of the reverse relativistic $\gamma$ functor is applied to study
high-frequency part of spectrum of electromagnetic waves propagating
perpendicular to the external magnetic field. The thermal effects considered
for the temperatures close to the rest energy of electrons considerably change
the dispersion equation in compare with the nonrelativistic temperatures.
Analytical analysis of the changes is presented.
