Thermal conduction in granular materials is mainly dominated by volumetric fraction of constituents, minerals that consist of grains, grain size distribution, and fine contents. Even though widely used empirical and semi-empirical correlations for thermal conductivity of granular materials capture these governing factors, the effect of applied stress appears overlooked and is rarely incorporated into the thermal estimation. This study presents the stress-dependent thermal conductivity evolution of granular materials using the discrete element method (DEM) in conjunction with the 3D thermal network model. A series of loading (loading, unloading, and reloading) is applied under isotropic stress and K0 conditions for the numerically synthesized assemblies whose grain size distribution varies. Results highlights that not only the effective thermal conductivity increases nonlinearly with stress and but also its incremental ratio varies with the stress in the direction through which heat flow takes place. The nonlinear anisotropic increase and engineering implications of stress-dependent thermal conduction are discussed.