We investigate the heat transfer rates through a contact network of a sheared granular material using the Discrete Element Method (DEM). The tool ParScale enables us to study intra-particle transport processes, and the DEM solver LIGGGHTS is used to carry out the simulations. A plethora of dimensionless parameters is investigated, in order to picture different phenomena occurring near the jamming point (e.g., solidification) of a sheared granular material. Thereby, the main outcome is the quantification of thermal fluxes which occur due to (i) conduction in case of particle-particle collisions, as well as (ii) convection due to random particle motion. Also, the transferred heat between the particles and the ambient fluid is analysed. In addition, we analyse the phenomenon of crystallization, and the effect on the thermal transport rate in the granular material. Furthermore, we demonstrate that the ordering process, and hence the heat transport rate, can be controlled by adjusting the coefficient of friction of the granular material. Again, measured thermal fluxes are exploited to decide whether a system is crystallized or not.