We present two preconditioners about the preserving-symmetry finite volume element (SFVE) scheme for solving two-dimensional three-temperature radiation diffusion equations with strongly discontinuous coefficients. Both preconditioners involve a SFVE subsystem with respect to a simple coarse space and SFVE subsystems which are self-similar to the original SFVE system but embarrassingly parallel. We prove algebraic and parallel implementations of the developed PCG solvers, and provide the numerical results validating the aforementioned theoretical estimations and stating the good al-gorithmic and parallel scalabilities.