According to thermal diffusivity measurements, radiative heat transfer was considered to be responsible for a marked increase in the thermal conductivity of urania upon melting. Based on measurements of the optical constants of liquid urania, the radiative contribution to the thermal conductivity has been calculated by means of the Rosseland approximation. Liquid urania proves to be opaque to thermal radiation up to temperatures exceeding 4000 K. The radiative contribution to the thermal conductivity remains below 0.7 W/mK-1. An increase in the radiative heat transfer of a core melt with increasing temperature can be excluded.