A numerical method based on particle tracking and random walk is applied to convective heat transfer. The technique is useful in problems with high Peclet numbers in which the velocity field is known from other means. Advection is simulated by particle motion along a pathline, and diffusion by random walk. The advection time and diffusion distance determine the Peclet number. Several examples of the computation of temperature field and wall heat fluxes in advection-dominated flows for which analytical solutions are known are provided as illustrations of the method.