  The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang,
J. Comput. Phys., 229, pp. 7747--7764, 2010], originally developed for
multiscale gas dynamics problems, is applied in this paper to a linear kinetic
model of radiative transfer theory. While such problems exhibit purely
diffusive behavior in the optically thick (or small Knudsen) regime, we prove
that UGKS is still asymptotic preserving (AP) in this regime, but for the free
transport regime as well. Moreover, this scheme is modified to include a time
implicit discretization of the limit diffusion equation, and to correctly
capture the solution in case of boundary layers. Contrary to many AP schemes,
this method is based on a standard finite volume approach, it does neither use
any decomposition of the solution, nor staggered grids. Several numerical tests
demonstrate the properties of the scheme.
