Hyperbolic material has attracted significant attentions due to its anisotropic hyperbolic dispersion which allows for propagation of hyperbolic phonon polaritons, especially the high-k modes within the Reststrahlen bands (RBs) in infrared (IR). Our study reveals that these high-k hyperbolic phonon polaritons also enabled radiative heat transfer inside hyperbolic materials, which has the potential to be utilized for thermal management. In this work, we quantitatively explore radiative transfer in hyperbolic materials. We first use Fourier Transfer Infrared microscopy (FTIR) to measure polarized reflection along in-plane principal axes to determine the permittivity (dielectric constants) along all principal axes. Then, a many-body radiative transport model is employed to compute an equivalent thermal conductivity by radiation, called radiative thermal conductivity. Our results show that radiative heat transfer in hyperbolic materials is greatly enhanced by hyperbolic phonon polaritons within RBs whose spectral radiative heat flux can be more than six orders of magnitude larger than that of blackbody. The temperature-dependence of radiative transfer is also of interest and is investigated. Temperature-dependent permittivity is measured using FTIR from room temperature to 600 K. It is found that the radiative transfer by hyperbolic phonon polariton increases as the temperature increases, and accounts for a significant portion of the total thermal transport at elevated temperatures.