A method for improvement of the negative hydrogen ion yield in the electron cyclotron resonance source with driven plasma rings is proposed. In the source the negative ion production is realized in two stages. First, the hydrogen molecules are excited in collisions with plasma electrons to high-laying Rydberg and high vibration levels in the plasma volume. The second stage leads to negative ion production through the process of repulsion attachment of lowenergy electrons by the exited molecules. The low-energy electrons originate due to the bombardment of the plasma electrodes surface by ions of the driven ring. The calculation data on the negative ion production demonstrate that additional very low-energy thermoelectrons significantly enhance the negative ion production. As a first step to investigate the phenomenon the tungsten filaments were placed in the source. It is found that the heating of the tungsten filaments placed in the source chamber improves the discharge stability and extend the pressure operation range. The filaments system heating is accompanied by enhancing the extracted current by 5%. The low efficiency of the filament thermoelectrons owes to the fact that they provides conditions for the negative ion formation in the plasma volume where the extraction field does not penetrate.