A Lagrangian stochastic model has been formulated to simulate the dispersion of Brownian (submicron-sized) particles in turbulent flows and their deposition onto adjacent flow boundaries. The model is applied to the prediction of Brownian-particle dispersion and deposition under non-isothermal conditions. Thermophoresis is shown to arise naturally from the modelling approach which is based upon a natural extension of Thomson's (1987, Journal of Fluid Mechanics, 180, 529-556) well-mixed condition. In accordance with results present in the literature, it is found that thermophoresis has a significant impact upon model predictions for the deposition of Brownian particles from fully developed turbulence onto hydraulically smooth surfaces. (C) 2005 Elsevier Ltd. All rights reserved.