The steady-state behavior of a ceramic slab under microwave heating by transverse magnetic illumination is analyzed. Local bifurcation techniques are applied to a one-dimensional model to classify the region of parametric sensitivity (or thermal runaway). It is observed that for a certain set of parameters, there are periodically recurring ranges of slab thickness for which thermal runaway may be avoided. The runaway dependence on other parameters critical to the operation of the process is also studied. The results presented here may be used to prevent thermal runaway in microwave heating of ceramics.