  We present a transport equation for the incoherent propagation of radiation
inside a quasi-resonant atomic gas at low temperature. The derivation is based
on a generalized Bethe-Salpeter equation taking into account the motion of the
atoms. The obtained equation is similar to the radiative transfer equation. It
is solved numerically by an original Monte Carlo approach in the case of a slab
geometry. The partial frequency redistribution caused by the small velocity of
the scatterers make the emitted flux outside the system and the energy density
inside the medium to behave differently than in the case of complete frequency
redistribution. In particular, the long time dependence of the specific
intensity (escape factor) is slightly different from the Holstein prediction.
