  In this paper we study the distribution of the temperature within a body
where the heat is transported only by radiation. Specifically, we consider the
situation where both emission-absorption and scattering processes take place.
We study the initial boundary value problem given by the coupling of the
radiative transfer equation with the energy balance equation on a convex domain
$ \Omega \subset \mathbb{R}^3 $ in the diffusion approximation regime, i.e.
when the mean free path of the photons tends to zero. Using the method of
matched asymptotic expansions we will derive the limit initial boundary value
problems for all different possible scaling limit regimes and we will classify
them as equilibrium or non-equilibrium diffusion approximation. Moreover, we
will observe the formation of boundary and initial layers for which suitable
equations are obtained. We will consider both stationary and time dependent
problems as well as different situations in which the light is assumed to
propagate either instantaneously or with finite speed.
