Experimental investigations of thermophoretic forces acting upon aerosol particles in the atmosphere are being carried out in cooperation between the Institute of Atmospheric Sciences and Climate (ISAC) of the National Research Council (CNR) of Italy, the Department of Physics of the University of Ferrara, Italy, and the Microgravity Research Centre of the Universite Libre de Bruxelles, Belgium. This experimental task, aiming at understanding the behaviour and distribution of aerosol particles in the atmosphere, is paralleled by the development of a computer program simulating the thermophoretic forces with the Direct Simulation Monte Carlo (DSMC) method of molecular dynamics. Purpose of the computational effort is a better understanding of the experimental data and analysis of thermophoretic forces in regimes, like intermediate Knudsen numbers, where experimental data are not available. The articles explains the details of the application of the DSMC method to the simulation of thermophoretic forces and of the calculation of the temperature distribution in the simulated aerosol particle, which is essential to compute the energy exchanged between particle and colliding air molecules. Preliminary computational data are compared with experiments, providing information about the suitability of the computational approach followed. Order of magnitude of computed thermophoretic velocities agree fairly with experimental data. To reduce statistical scattering of computed results it would be necessary to simulate a larger number of sample molecules and perform three-dimensional simulations with massive parallel computers.