A computational model of a Buncher cavity for millimetric klystron following a Multiphysics approach is proposed in this paper. At these narrow dimensions, the device is critically exposed to multiple physics effects, due to the power dissipations and external environment, influencing the electromagnetic performances. The cavity is integrated with a carbon nanotube cold cathode in order to reduce thermal expansion and cooled by an opportune airflow that regulates the temperature distribution to compensate the resonant frequency shift. Electromagnetic fields and scattering parameters have been tested in operative conditions by concurrent computation of coupled thermodynamic, fluid dynamic, structural mechanics and electromagnetic simulations. This approach has suggested the appropriate materials and geometrical shapes.