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The high-power millimeter-wave beams that can be generated by CW gyrotrons represent a promising energy source for rapid high-temperature processing of materials. A program is under way at the Naval Research Laboratory to investigate the heating of ceramic tubes and cylinders using an 83-GHz beam for joining and sintering applications. In this paper, we discuss the scattering and absorption of microwave power by a ceramic cylinder and calculate the resulting temperature profile. The analysis accounts for the temperature dependence of the dielectric properties, an effect that can dramatically alter the microwave coupling during the heating process. In the process under investigation, the cylinder is rotated to promote azimuthally uniform heating so that only the radial dependence of the dielectric properties needs to be included.