An unfavourable influence that degrades the performance of any millimeter wavelength radio telescope is the deformation of the reflector surface due to temperature differences in the supporting backup structure. To avoid, or at least reduce this influence, the backup structures are typically protected by a rear side cladding, insulation at the panel inner side, and ventilation or climatization of the air inside the backup structure. During the design of a mm-wavelength telescope, the layout of a thermal protection system is made, based on experience gained on other telescopes, and on thermal model calculations of the complete backup structure. The available thermal programs allow today the construction of a multi-layered backup structure model, consisting of the backup structure tube network, without and with ventilation/climatization, the panels, insulation behind the panels, and the rear side cladding. We provide a guideline for the construction of such a multi-layered thermal model, and demonstrate that realistic temperature gradients across and through a backup structure can be calculated. These gradients can be used in a finite element model to calculate the reflector surface deformations, which can be used in a diffraction program to calculate the radio beam pattern.