  The high-frequency part of spectrum of electromagnetic waves propagating
parallel to the external magnetic field is considered for the macroscopically
motionless plasmas with the relativistic temperatures $T\sim m_{e}c^{2}$, where
$m_{e}$ is the mass of electron, $c$ is the speed of light. The analysis is
based on the novel hydrodynamic model based on four equations for the material
fields which can be combined in two four vectors. These material fields are the
concentration and the velocity field \emph{and} the average reverse
relativistic $\gamma$ functor and the flux of the reverse relativistic $\gamma$
functor. In the nonrelativistic regime we have three waves (the ions are
assumed to be motionless). Strong thermal effects lead to a coefficient in
front of cyclotron frequency which decreases the effective contribution of the
cyclotron frequency. At $T=0.1m_{e}c^{2}$ we have a decrease of area of
existence of fast magneto-sound wave from the area of the large frequencies.
While the area of existence of extraordinary waves becomes larger towards
smaller frequencies. The strong magnetic field limit $\mid\Omega_{e}\mid >
\omega_{Le}$ additional wave appears with frequency below thermally decreased
cyclotron frequency, where $\mid\Omega_{e}\mid$ is the electron cyclotron
frequency, and $\omega_{Le}$ is the Langmuir frequency. Further increase of
temperature leads to the disappearance of fast magneto-sound wave and to the
considerable increase of area of existence of extraordinary towards smaller
frequencies.
