We study a finite volume solver for radiation hydrodynamical models in two space dimensions. For nonlinearity of radiation pressure and radiation energy, it is not a trivial task to develop a numerical scheme for radiation hydrodynamics compared to Euler equations. The current strategy is that the convective part is solved by MUSCL-Hancock schemes, while the diffusive part is handled through an alternative form of TR/BDF2 (trapezoidal rule with second order backward difference formula) method. An asymptotic analysis for the grey nonequilibrium diffusion model in time is presented. Numerical experiments are given to show performance of the IMEX scheme.