Within the thermal wave model (TWM) description, an investigation was made of the longitudinal instability properties of a coasting high energy charged particle beam, where the interaction between the beam and its surroundings is characterized in terms of a complex impedance. The analysis is shown to correctly reproduce the characteristic features of the coherent instability as obtained previously by conventional techniques based on the Vlasov equation for the beam distribution. The results further validate the TWM approach as a consistent alternative description for analyzing the dynamics of high energy charged particle beams.