We have been proposed functionally graded material type electromagnetic wave absorbers (FGM type EM-wave absorbers) for the improvement in absorption performance and material strength. In this study, we investigate a plane-strain thermoelastic problem of the FGM type EM-wave absorbers for a hollow cylinder subjected to irradiation power and convective heat load. The FGM layer with graded composition is considered as a multilayered layer. We present the analytical solutions of electromagnetic fields and irradiation power distributions in the absorbers. Temperature fields are analyzed by modifying Vodicka's method. Elastic thermal stress and thermal displacement are also analyzed based on the stress function method. Numerical calculations are carried out for the FGM type cylindrical absorbers with absorption layers composed of epoxy resin matrix and conductive titanium oxide particles. The temperature and thermal stress distributions in the FGM type cylindrical EM-wave absorbers subjected to asymmetrical heating are quantitatively evaluated.