The subject of this paper was to develop a mathematical model of a non-contacting face seal describing the phenomenon of the heat transfer in the system: sealing rings fluid film. The function of non-contacting face seals used in rotor machines is to separate the working agent from the external environment. The nature of operation of non-contacting face seals allows the fluid to leak through the clearance not bigger than a few micrometres. During the operation of the rotor machine between the co-operating rings, an intense conversion of mechanical energy into-heat occurs. At first, the heat flux generated in the fluid film is channelled to the sealing rings and then to the surrounding fluid. The solution of the presented model was conducted with the use of analytical methods for the direct and the inverse heat transfer problem. The distribution of the temperature fields in the sealing rings for the direct heat transfer problem was determined with the use of Fourier-Bessel series as the surface function of two variables (r,theta) for the cross-section of a ring. The inverse heat transfer problem was solved with the use of Trefftz functions. The presented computational methods allow a more detailed identification of the phenomenon of the heat transfer in non-contacting face seals and indicate a direction of further research and preparation of new computational methods. (C) 2015 Elsevier Ltd. All rights reserved.