A thermal plasma is studied accounting for both impact ionization, and an electromagnetic field. This plasma problem is modeled based on a system of Boltzmann type transport equations. Electron-neutral collisions are assumed to be much more frequently elastic than inelastic, to complete previous investigations of thermal plasma . A viscous hydrodynamic/diffusion limit is derived in two stagesdoing an Hilbert expansion and using the  Chapman-Enskog method. The resultant viscous fluid model is characterized by two temperatures, and non equilibrium ionization. Its diffusion coefficients depend on the magnetic field, and can be computed explicitely.