We present a theoretical framework to study the thermal responses of one-dimensional multilayered systems, functionally graded solid media, and porous materials. The method for thermal analysis resorts to non-Fourier heat conduction theories including three-phase-lag, dual-phase-lag, and hyperbolic heat conduction. The graded media are modeled as multilayered systems displaying finite numbers of layers. For each homogenous layer, the differential equations of heat conduction describing the wave-like three-phase-lag are solved in closed-form in the Laplace domain. Solutions accounting for proper interfacial and boundary conditions are first presented to describe the thermal behavior of heterogeneous solids and porous media. Transient temperature and heat flux are obtained in time domain via fast Laplace inversion. We then apply the solutions obtained with each heat conduction theory to one-dimensional media and compare their thermal behavior. Finally, maps are presented to visualize the thermal responses of cellular materials, functionally graded cellular materials, and multilayered systems. For the latter, particular attention is devoted to investigate the impact of key attributes defining graded media, such as layer bond imperfections and material heterogeneity. (C) 2014 Elsevier Ltd. All rights reserved.