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We develop a computationally efficient method for the theoretical analysis of thermophoresis of nanoparticles and adatoms on crystalline surfaces (thermal tweezers) for efficient parallel nanofabrication. The analysis of surface diffusion of particles or adatoms in the presence of strong temperature gradients is conducted through the direct determination of probability distributions for diffusing particles, using the numerical solution of the Smoluchowski diffusion equation with varying (temperature-dependent) diffusion constant. The local values of the diffusion constant are determined from the Fokker–Planck equation for the considered crystalline potential of the substrate and local temperature. Steady-state and nonsteady-state particle distributions on the surface are obtained and analyzed in the presence of optically-induced strong temperature gradients. Detailed comparison of this approach with the previously obtained results from the Monte Carlo simulations of the Langevin equation is conducted, demonstrating high computational efficiency, and accuracy of the new method in the high-friction regime. Applicability conditions for the developed method are also determined and discussed. [ABSTRACT FROM AUTHOR]