We have measured optical transmittance spectra in rhyolitic obsidian samples in the wavelength range λ=380-5500 nm and at temperatures T from 19¿-1145¿C, above and below the softening point. From the transmittance, we calculated the absorption coefficient α(λ,T) and the radiative thermal conductivity KR(T). KR ranges from 3¿10-3 cal cm-1s-1K-1 (1.2Wm-1K-1) at 700¿C to 12¿10-3 cal cm-1s-1K-1(5Wm-1K-1) at 1145¿C. The 700¿C value is comparable with lattice thermal conductivity KL of about 4¿10-3 cal cm-1 s-1K-1(1.7 Wm-1K-1). Removing scattering effects due to bubbles from the transmittance spectra by lowering the absorption baseline increased KR to 20¿10-3 cal cm-1 s-1 K-1(8.4Wm-1K-1) at 1145¿C. Because scattering bubbles is likely to be small in confined magmas, these numbers are probably minimum values for KR and indicate that in active plutons radiative heat transport could be greater than lattice conductivity by more than a factor of 2 at 1000¿C. Thus melting markedly strengthens KR, and radiative heat transport is probably the dominant component of the total conductivity K=KL+KR in silicic magmas. These relatively large values of K can be applied to models of the thermal evolution of magma bodies and to cooling of intrusives.<