<p>Heat transfer and electrical transport in granular materials are important phenomena in many engineering applications. The discrete element method (DEM) is commonly used to simulate conduction in such media. The DEM usually employs explicit time integration algorithms due to their computational efficiency. The first-order differential equations describing transient thermal or electric problems in the DEM are commonly solved using the forward Euler explicit solution scheme. All explicit schemes have a serious disadvantage of conditional stability, which limits the time step length. The present paper introduces the super-time-stepping (STS) acceleration method into the DEM framework for transient thermal and electric problems governed by the first-order differential equations. The STS idea consists of relaxing the stability condition for single steps and imposing the stability on a cycle of steps (substeps), making up the so-called superstep. The length of the superstep is much longer than the critical time step of the standard explicit time integration. This is an established method for solving parabolic differential equations, commonly recognized for its advantages over the standard explicit time integration. Despite the efficiency, its application within the DEM framework remains unexplored. Herein, STS is applied to thermal and thermoelectric simulations. The efficiency and accuracy of the STS scheme for different combinations of parameters are investigated. The results demonstrate that speedup of up to 15 is achievable without compromising accuracy. The strong performance justifies a wider applicability of the STS acceleration scheme in the DEM for problems governed by the first-order differential equations.</p>