Methods of thermodynamics of irreversible processes are presented within the framework of the Burgers‐Pipkin solution of the Boltzmann transport equation. The thermionic energy converter is treated as a thermocouple and analyzed by the nonequilibrium thermodynamic methods which are developed.Following a general treatment, the cesium diode is treated as a specific example. Detailed calculations are made of the thermal conductivity and the electrical conductivity, as well as the ratio. In making the calculations, contributions from the electrons, positive ions, and neutral particles, are considered as well as interactions among the various types of particles. Binary interactions between the neutral particles, collective (Coulomb) interactions among charged particles, and (quantum‐mechanical) collisions between electrons and neutral particles are taken into account. Each type of interaction has its appropriate effect on the thermal and electrical conductivities.A brief discussion of the results and implications of the analysis is given, along with a reiteration of the assumptions and the limitations of the calculation.