Porous media are commonly found not only in the nature but also in industries. Furthermore, porous media is an important research prototype for a diversity of disciplines. So far a REV (representative elementary volume) scale lattice Boltzmann (LB) model has been proposed and popularly used for investigation on heat transfer in porous media. Unfortunately, such model suffers from a serious drawback that it can not address an investigated domain where the heat capacitance (the product of density and specific heat capacity) of porous media varies spatially obviously. Such deficit restricts dramatically its applicable range. The purpose of the present work is to remedy such serious shortcoming in a simple way. Numerical validation demonstrates the capability and reliability of the present model. In order to clearly show the advantage of the present model, here a single-relaxation-time LB model is taken as an example to illustrate how to remedy the shortcoming of previous models. Its multiple-relaxation-time counterpart can be established straightforwardly in the same way. (C) 2017 Elsevier Ltd. All rights reserved.