This work deals with the modeling of fusion plasma by bi-temperature fluid models. First, using non-dimensional scaling of the governing equations, we give the assumptions leading to a bi-temperature model. Then we describe a finite volume method on non-structured meshes to approximate the solutions of this model. The method relies on a relaxation scheme to solve the Riemann problem at the interfaces. The description of the finite volume method that uses the strong conservative form of the equations is given both in Cartesian as well as in cylindrical coordinate systems useful to compute flows inside a torus. Several numerical tests in Cartesian and cylindrical coordinate systems and in different geometries are presented in order to validate the numerical method.