Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. The planar Multipole Resonance Probe (pMRP) offers this ability and is a suitable diagnostic tool to monitor plasma processes in industrial applications. The analysis of the fluid-model of the pMRP led to a formula for the resonance frequency, which can be used to determine the electron density. To widen its field of application in terms of measuring the electron temperature additionally to the electron density another relation between the electron temperature and second resonance parameter is needed. Such a parameter is given by the half width of the resonance peak, which represents the damping of the system. In low pressure plasmas the half width depends not only on collisional damping, but also on collisionless damping. To investigate the influence of collisionless damping on the half width and to determine a relation between the half width and the electron temperature a kinetic model is required. Such a model of the pMRP, based on functional analytic methods, will be presented in this work and the result of the explicit expansion of the admittance will be shown.