Calculations of translational self-diffusion coefficient in free-standing smectic films during a series of layer-thinning transitions as the temperature is raised above the bulk smectic-A-isotropic transition have been carried out. A molecular model based upon the random walk theory is applied for calculating the translational diffusion coefficient (TDC) D_{∥} across the smectic film both in the bulk of the film, as well as in the vicinity of the bounding surfaces. Calculations of D_{∥} require the set of the orientational and translational order parameters (OPs) which have been obtained by using the extended McMillan approach with anisotropic forces. The effect of E on the orientational and translational OPs, as well as on the TDC of smectic films has been investigated. A reasonable agreement between the theoretically predicted and the experimentally obtained data on the TDC in the bulk of the partially fluorinated H10F5MOPP film has been obtained. We also found, in agreement with the experimentally observed behavior of D_{∥}(N)(N=25,13,11,10), that the translational diffusion coefficient in the bulk of the film gradually increases as the film thickness N is decreased.