The present investigation aims at numerically simulating the temporal energy transport for incompressible flows through a packed bed. The governing equations are formulated according to the volume averaging method. The generalized momentum equation which accounts for the inertial and viscous forces was used to carry out this research, whereas the two-energy equation model was used for simulating the energy transport. The implications of the non-Darcian terms and the thermal dispersion effects on the transient energy transport were explored. Error maps were introduced for a wide range of flow conditions and bed configurations. In addition, the investigation also tackles the applicability of the local thermal equilibrium condition and the one-dimensional approach for studying the thermal response in packed bed.