The optical absorption spectra of natural single-crystal and polycrystalline olivine (mg1.84Fe0.16SiO4) have been measured in the wavelength range 300--8000 nm at temperatures ranging from 300 to 1700 K and under oxygen fugacity well within the sample stability field. The absorption significantly increases with increasing temperature due to a regular broadening of both crystal field and multiphonon lattice vibrational absorption bands; these are the principal absorption bands in the spectral region involved in radiative heat transfer. In the 'window' region between these bands the absorption coefficient increases from near zero at 300 K to about 10--15 cm-1 at 1700 K. Under mantle conditions the radiative thermal conductivity (KR) calculated from the olivine single-crystal spectra increases from near zero at 300 K to about 5¿10-3 cal/cm s K (2W/m K) at 1700 K and is only weakly dependent on temperature above 800 K. Our determination of KR is 10--20% lower than previous estimates based on absorption measurements under different experimental conditions. In polycrystalline (dunite) samples the transmission decreased substantially with temperature cycling due to scattering at intergranular interfaces created by differential thermal expansion.