A model of the low-current gas discharge in a mixture of argon and mercury vapor in the presence of a thin insulating film on the cathode surface is proposed. The model takes into account that in such a mixture a substantial contribution to the ionization of the working gas can come from the ionization of mercury atoms during their collisions with metastable excited argon atoms. In the discharge, positive charges accumulate on the film surface, creating an electric field in the film sufficient to cause field emission of electrons from the cathode metal substrate into the insulator. Such electrons are accelerated in the film by the field and can escape from it into the discharge volume. As a result, the effective yield of ion-electron emission from the cathode increases. The temperature dependences of discharge characteristics are calculated and it is shown that, due to a rapid decrease in the concentration of mercury vapor in the mixture with decreasing temperature, the electric field strength in the discharge gap and the discharge voltage increase. The presence of a thin insulating film on the cathode can result in an improvement in its emission characteristics and a significant reduction in the discharge voltage. This causes a decrease in the energies of the ions and atoms bombarding the cathode surface, and, consequently, in the intensity of cathode sputtering in the discharge.