A numerical analysis of the rarefied gas flow caused by a temperature gradient in the direction tangential to a wall through a planar channel of finite length is carried out based on the nonlinear Shakhov model of the Boltzmann kinetic equation. The Maxwell diffuse and Cercignani-Lampis gas-surface interaction models are provided as a boundary condition at solid walls. An implicit scheme for solution of the S-model kinetic equation was applied and the algorithm has been optimized for the use of massive parallelization in both physical and velocities spaces. The competition between rarefaction, gas-surface scattering model and temperature gradient effects on a gas flow is discussed in terms of both mass flow rate and streamwise heat flux. A comparison with available literature results has been carried out and showed a good agreement. It was found that the temperature gradient as well as the gas-surface scattering dynamics play a significant role for the highly rarefied gas flow, beginning from the transition flow regime. At the same time, under certain gas-surface scattering conditions a change of the value of temperature gradient does not affect the heat flux. For the weakly rarefied flow the temperature gradient effect on the mass flow rate is small for any gas-surface scattering condition, while the heat flux does not depend neither on value of temperature gradient nor choice and details of gas-surface scattering dynamics. (C) 2015 Elsevier Ltd. All rights reserved.