  The process of Compton scattering $\gamma e^{\pm} \to \gamma e^{\pm}$ in a
strongly magnetized medium of arbitrary temperature and zeroth chemical
potential was considered. The analytical expressions for the partial cross
section in the small concentration limit of the electron-positron plasma are
obtained. The numerical estimations for the partial probabilities of this
process are presented by taking into account the photon dispersion in a strong
magnetic field and charge-symmetric plasma of arbitrary temperature. The
comparision of the scattering probability with photon splitting in a plasma was
investigated. The astrophysical applications of the obtaining results are
considered.
