Microwave processing presents a relatively new heating source for a large variety of processes and materials. Depositing microwave energy volumetrically, microwave heating appears as a good alternative for sintering ceramics by decreasing the process time, offering better energy efficiency, but also diminishing thermal gradients inside the materials, producing more uniform heating, and therefore better mechanical properties. However, the strong temperature dependence of the ability to store or absorb the microwave energy of the material, and its variation of several orders of magnitude when the temperature increases, makes the control of the temperature of the material problematic and can lead to thermal runaway. The research reported in this thesis uses numerical modeling to investigate the feasibility of temperature control for continuous microwave processing of thermal runaway materials, applied specifically to alumina and zirconia fibers. Using a one-dimensional model valid for any continuous material moving through a microwave cavity, we were able to demonstrate control of the temperature inside the fiber by using a new approach of controlling the distribution of the energy deposited along the fiber. We were able to determine an electric field strength profile to generate the desired temperature profile for both fibers.