This paper is devoted to the study of the bitemperature Euler system in a polyatomic setting. Physically, this model describes a mixture of one species of ions and one species of electrons in the quasi-neutral regime. We firstly derive the model starting from a kinetic polyatomic model and performing next a fluid limit. This kinetic model is shown to satisfy fundamental properties. Some exact solutions are presented. Finally, a numerical scheme is derived and proved to coincide with an approximation designed in [3] and extended to second order and two space dimensions in [6]. Some numerical tests are presented.