To investigate the internal temperature profiles produced in ceramic workpieces during microwave processing we analyze the heating of ceramic cylinders by a plane-wave RF beam for frequencies in the microwave and millimeter-wave regimes. The analysis includes the temperature dependence of the dielectric properties, an effect that can dramatically alter the microwave coupling during the heating process. To approximate the continuous variation of dielectric properties and temperatures, the cylinder was subdivided into thin tubular regions. The nonlinear heat conduction equation is solved by an iterative process