The present paper is dedicated to an application of the discrete element method (DEM) to study heat transfer by conduction in continuous and heterogeneous media. Our objectives are threefold. First, we aim to set up an original process to generate a Voronoi tessellation based on a granular assembly. This efficiently provides suitable areas of transmission and a representative volume to each particle which are considered to model heat transfer in the continuous medium. Second, a proper expression of the heat flux density is derived from Fourier's law at a mesoscopic scale represented by polygonal elements called specimens. In this context, investigations led on the sensitivity of the heat flux density distribution with respect to the number of particles within polygonal specimens are performed. Finally, we investigate the suitability of the DEM-based approach to yield thermal properties and heat flux density fields in continuous and heterogeneous media. Two heterogeneous configurations are tested, namely a classic single inclusion problem and a random particulate composite material for which the issue of representative volume element is also discussed. Results exhibit a good agreement with other numerical approaches such as the finite element method and the fast Fourier transform based technique.