Current experimental results indicate that sonoluminescence is largely thermal in origin, with the spectra showing a direct relation between luminous intensity and the temperatures generated inside the collapsing cavitation bubbles. In the present paper, the strong dependence of the luminous intensity on the nature of the gas dissolved in the liquid is explained in terms of thermal conduction. Provided the cavitation bubbles are sufficiently small, loss of heat from the bubble into the liquid can significantly reduce the temperatures attained during collapse, so that there is a consequent reduction in the luminous intensity. This process is demonstrated analytically by means of a numerical solution of the equations of motion of a gas inside a collapsing cavitation bubble. The agreement between the theory and the observed luminous intensities for different dissolved gases is good.