A microwave heating process implies the direct conversion of electromagnetic energy into heat. In this work, we simulate microwave heating (2450 MHz) of a functionally graded material (FGM). FGMs are novel composites with gradual variations in their compositions and structures throughout their volume. Such material, for our case, comprises three-phase heterogeneous concentric spheres (i.e., a core-shell structure) where thermal properties, such as conductivity and specific heat, follow a space-continuous function valid for the entire heterogeneous sphere. We express these functions as a power series in terms of temperature and three-dimensional position. We also consider that the electric permittivity and electric permeability coefficients of these shells are constant. Similarly, the volumetric heat flow is position- and time-dependent. Hence, the resulting mathematical model consists of three time-dependent coupled partial differential equations, which we solve numerically through a finite element approach. We model the composite sphere, assuming that it resides within an electromagnetic cavity and that it rotates upon its axial symmetry axis to allow uniform heating throughout the outer surface. We include numerical simulations of these thermal effects, individually and in combination. The simulation data revealed a marked dependence on the thermal properties and the type of microwave heating (internal generation), which affect the resulting temperature profiles and heat fluxes.