In classical theory of porous media, a local thermal equilibrium between fluid phase and solid phase is assumed. According to this theory, the fluid and solid temperatures reach an equilibrium temperature value rapidly. However, in porous media, the rate of heat transfer between the fluid and solid may not be fast enough to achieve a local thermal equilibrium (LTE) due to their thermal diffusion properties. Therefore, this paper examines the importance of local thermal non-equilibrium (LTNE) in porous media with conductive heat transfer. The LTNE is constituted by energy equations and defines distinctive temperature profiles for both the solid and fluid phases. The Laplace transform and Stehfest algorithm methods have been employed in formulating an exact solution. Using the weighted average method, a temperature for the porous media is defined. Subsequently, the model is applied to a cylindrical hole subjected to a uniform temperature in an infinite porous medium (rock formation). The exact solution and transient temperature profile are the advantages of this model compared to existing LINE models. (C) 2018 Elsevier Ltd. All rights reserved.