  Relativistic thermal electrons moving in a large-scale magnetic field can
produce synchrotron radiation. Linear synchrotron polarization can also be
produced by the relativistic thermal electrons. In this paper, we utilize a
hybrid thermal-nonthermal electron energy distribution to calculate circular
synchrotron polarization. We further compute the radiative transfer of the
synchrotron polarization in the optical and radio bands when we consider the
contribution of the thermal electrons. We attempt to apply the polarization
results to some astrophysical objects, such as kilonova like AT
2017gfo/GW170817, the fast radio burst (FRB), the Gamma-ray burst (GRB)
afterglow, and the supernova remnant (SNR). The large optical depth of
radiative transfer effects the small polarization degrees of these populations
when the media surrounding the synchrotron sources take heavy absorption to the
polarized photons. We need a strong magnetic field in our model to reproduce
the linear and circular polarization properties that were observed in FRB
140514. This indicates that FRBs have a neutron star origin.
