The paper describes the post-impact thermal conduction of regular closed-cell cellular structure with gaseous fillers due to the dynamic compression. Two different but subsequent computational analyses have been carried out for this purpose. To define the behavior of the cellular structure under compressive dynamic loading, a unit volume element of the cellular structure has been analyzed with the explicit finite element code LS-DYNA by considering a strongly coupled interaction of the cellular structure base material with the gaseous pore filler. The resulting deformed cellular structure has then been imported in the finite volume code ANSYS CFX 10.0 for further weakly coupled thermal-structural analyses of post-impact heat conduction through the base material and filler gas. The increased temperature and pressure of the filler gas after compressive impact loading from the initial analyses have been used as initial conditions for the thermal analyses, where only the heat conduction due to the gas compression has been taken into account. This paper considers only the closed-cell cellular structure with two different relative densities and air inside the pores. Computational simulations have shown a low overall temperature increase of the cellular structure due to filler gas compression. The temperature increase of the base material is expected to be higher at lower relative densities. The presented procedure illustrates a convenient approach to solving strongly coupled fluid-structure interaction problems by considering also a weakly coupled thermal-structural solution, which can be used for a wide range of engineering applications.