The production of carbon fibers based on Polyacrylonitrile (PAN) precursor fibers is a very energy intensive process. In order to increase the energy efficiency, microwave plasma processes and, alternatively, dielectric heating with microwaves are in the focus. In this latter case, the knowledge of the dielectric properties over temperature is the key in the design of an appropriate microwave heating system. A measurement system was developed that is capable to monitor in-situ the change of the dielectric properties during the stabilization process of the PAN fiber. First results show that the loss tangent of the PAN fiber is strongly varying with temperature. Additionally, the dielectric properties are changing during the stabilization process due to the chemical transformation.