Microwave processing of ceramics has seen a growth in research and development efforts throughout the past decade. One area of interest is the exploration of improved heating control through experiments and numerical modeling. Controlled heating may be used to counteract non-uniform heating and avoid destructive phenomena such as cracking and thermal runaway. Thermal runaway is a potential problem in materials with temperature dependent dielectric properties. As the material absorbs electromagnetic energy, the temperature increases as does its ability to absorb more energy. Controlled processing of the material may be achieved by manipulating the applied field. The purpose of this research is to model the interaction of the EM-field with a thin ceramic fiber to investigate possible mechanisms that may affect the heating process. The fiber undergoes microwave heating in a single-mode resonant applicator. Maxwell's equations for the fields within the cavity are solved using mode-matching techniques taking into account the field interaction of the fiber and an arbitrarily shaped coupling aperture. Effects of varying the aperture shape on the field distribution are explored. The coupled nature of the electromagnetic solution with the material's temperature-dependent properties, including an analysis of non-uniform heating, is also discussed.