  In this paper, we study the diffusive limit of the steady state radiative
heat transfer system for non-homogeneous Dirichlet boundary conditions in a
bounded domain with flat boundaries. A composite approximate solution is
constructed using asymptotic analysis taking into account of the boundary
layers. The convergence to the approximate solution in the diffusive limit is
proved using a Banach fixed point theorem. The major difficulty lies on the
nonlinear coupling between elliptic and kinetic transport equations. To
overcome this problem, a spectral assumption ensuring the linear stability of
the boundary layers is proposed. Moreover, a combined $L^2$-$L^\infty$ estimate
and the Banach fixed point theorem are used to obtain the convergence proof.
This results extend our previous work \cite{ghattassi2020diffusive} for the
well-prepared boundary data case to the ill-prepared case when boundary layer
exists.
