An expression for the effective thermal conductivity λeff solids is derived, taking into account conduction by phonons and radiation, which displays the fact that λeff depends, generally in an involved manner, on temperature, temperature gradient, and the geometry of the experimental device. Explicit results are obtained in the limit of small temperature gradients, yielding a correction to the well-known radiation term proportional to T3, which is frequently employed to explain the observed rise of the thermal conductivity of certain semiconductors and insulators at elevated temperatures.