The mathematical model proposed in this paper describes thermal deformation processes in a non-contacting face seal. The processes include heat transfer phenomena in the rings sealing the radial clearance gap. In a non-contacting face seal with a flexibly mounted rotor (FMR), used, for instance, in a turbomachine, mechanical energy is instantly converted into heat. The heat flux generated in the film between the two faces travels through the structural elements to the surrounding fluid, causing asymmetric distributions of temperature. In the study, the mathematical model of the non-contacting face seal was solved analytically. The distributions of temperature in the rings were calculated using the Fourier Bessel series as a surface function of two variables (r,z) for a ring cross-section. The thermoelastic problems described with Navier's equations were solved by applying the Boussinesq functions and the Goodier thermoelastic displacement potential. The method used to solve the model is very complex and covers many theoretical and practical problems. These were included and described by presenting the solutions to the thermoelastic problems for non-contacting face seals. The results, especially those concerning fields of temperatures and thermal distortions, were compared with the results available in the literature and those obtained through numerical calculations presented in the author's previous papers. (C) 2014 Elsevier Ltd. All rights reserved.