  The thermal radiative transfer (TRT) equations form a system that describes
the propagation and collisional interactions of photons. Computing accurate and
efficient numerical solutions to TRT is challenging for several reasons, the
first of which is that TRT is defined on a high-dimensional phase space. In
order to reduce the dimensionality, classical approaches such as the P$_N$
(spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used
in the literature. In this work, we introduce a novel approach: the hybrid
discrete (H$^T_N$) approximation. This approach acquires desirable properties
of both P$_N$ and S$_N$, and indeed reduces to each of these approximations in
various limits. We prove that H$^T_N$ results in a system of hyperbolic
equations. Another challenge in solving the TRT system is the inherent
stiffness due to the large timescale separation between propagation and
collisions. This can be partially overcome via implicit time integration,
although fully implicit methods may become expensive due to the strong
nonlinearity and system size. On the other hand, explicit time-stepping schemes
that are not also asymptotic-preserving in the highly collisional limit require
resolving the mean-free path between collisions. We develop a method that is
based on a discontinuous Galerkin scheme in space, coupled with a semi-implicit
scheme in time. In particular, we make use of an explicit Runge-Kutta scheme
for the streaming term and an implicit Euler scheme for the material coupling
term. Furthermore, in order to solve the material energy equation implicitly
after each step, we linearize the temperature term; this avoids the need for an
iterative procedure. In order to reduce unphysical oscillation, we apply a
slope limiter after each time step. Finally, we conduct several numerical
experiments to verify the accuracy, efficiency, and robustness of the method.
