  We present detailed calculations of the electron thermalization by
synchrotron self-absorption accounting for cooling by Compton scattering. For
the first time, we solve coupled kinetic equations for electrons and photons
without any approximations on the relevant cross-sections and compute
self-consistently the resulting electron and photon distributions. The results
presented in this contribution may be applied to the magnetized coronae around
Galactic black hole accretion disks.
