Non-equilibrium energy transfer takes place for thin films when thermal disturbance is introduced. In this case, phonon transport inside the film governs the heat transport and temperature distribution in the film. In the present study an attempt is made to formulate and illustrate the phonon transfer in micro-scale silicon film of various shapes incorporating the non-orthogonal coordinate system. Successful application of the discreteordinates method to the solution of the equation for phonon radiative transport in non-orthogonal coordinates requires the application of various numerical techniques connected to the finite-difference method. The numerical solution of the equation for phonon transfer in non-orthogonal coordinate is introduced via adapting the discrete ordinate method. Phonon intensity distribution in the thin film is presented in terms of equivalent equilibrium temperature. It is found that film shape has significant effect on equivalent equilibrium temperature distribution inside the film. The validation study demonstrates that the code developed solving the equation for phonon transport is also applicable to the phonon transport in non-orthogonal coordinate system.