A fluid-plasma model description of the operation of a magnetic filter for electron cooling in gas-discharge plasmas is presented in the study. Directed to the use of weak magnetic fields in the sources of negative hydrogen ion beams for additional heating of fusion plasmas, hydrogen discharges have been considered. The numerical results obtained within a 2D-model are stressed. The 1D-model presented aims at showing the main trends whereas the results obtained within the 3D-model, also developed, confirm the 2D-model description. The models outline the importance of the transport phenomena: electron-energy and charged-particle fluxes. Reduction of the thermal flux across the magnetic field together with thermal diffusion and diffusion, acting in combination, is the basis of the electron cooling and of the spatial distribution of the electron density. Effects due to the (E × B)-drift and the diamagnetic drift form a fine spatial structure of the plasma-parameter variations.