The preferential motion of Brownian particles in a channel with heated or cooled walls was numerically simulated using a direct numerical simulation method, that is, the fluctuating-lattice Boltzmann method. The resulting focusing of Brownian particles on the channel centerline induced by heated walls is the focus of this study. The effects of wall temperature, fluid thermal diffusivity, and particle size and density were considered in terms of both the focusing efficiency and performance of Brownian particles. It was revealed that the particle focusing process follows a quadratic relationship with time at high wall temperatures or a linear relationship at low wall temperatures. For a fixed wall temperature, the focusing efficiency (i.e., how fast the Brownian particles aggregate) is dominated by the Prandtl number, that is, the relative importance of the heat transfer and momentum transfer in the fluid. Meanwhile, the Lewis number, that is, the ratio of the fluid thermal diffusivity to the particle self-diffusivity, controls the focusing performance (i.e., to what extent Brownian particles aggregate). The possible mechanisms behind this are discussed. Finally, the negligible influence of particle density on both the focusing efficiency and performance was revealed.