A theory of aerosol coagulation due to size-dependent thermophoresis is presented. This previously overlooked effect is important when local temperature gradients are large, the sol population is composed of particles of much greater thermal conductivity than the carrier gas, with mean diameters much greater than the prevailing gas mean free path, and an adequate "spread" in sizes (as in metallurgical mists or fumes). We illustrate this via a population-balance analysis of the evolution of an initially log-normal distribution when this mechanism dominates ordinary Brownian diffusion.