This article deals with the finite element (FE) modeling and dynamics analysis of bidirectional functionally graded (2D-FG) rotating shaft system considering temperature-independent (TID) and temperature-dependent (TD) material properties of shafts. Time-dependent two-dimensional (2D) temperature distribution of such shaft has been found using the finite difference method (FDM). Based on the first-order shear deformation theory, a three noded beam elements has been developed for the finite element (FE) modeling and dynamic analysis of such shaft systems. It has been observed from obtained results that dynamic responses have significantly been influenced by temperature variation, power-law index, and internal viscous and hysteretic damping. Communicated by Marat Z. Dosaev. © 2020, © 2020 Taylor & Francis Group, LLC.