A 1-D model for the simulation of transition from glow microdischarge to arc discharge with a thermionic cathode was built using COMSOL Multiphysics. The extended fluid model was coupled with the gas heating equation for the self-consistent simulation of discharge at atmospheric pressure in a wide range of currents. Both the secondary electron emission and the thermionic emission were taken into account simultaneously to allow for the transition. In order to properly account for thermionic emission, cathode heating was considered - heat flux equation was solved in a 1-D solid domain with heat fluxes on the cathode surface from the discharge domain used as boundary conditions. A thorough set of plasma-chemical reactions with account of molecular ions of argon was used. Using the external circuit allowed for obtaining stable solutions in a wide range of currents. By changing ballast resistance, the classical current-voltage characteristic of direct current discharge with transition from glow to arc was obtained. The distributions of such discharge parameters as charged and excited particle densities and fluxes, electron mean energies and temperatures, gas temperature, and electric potential were obtained for microdischarge, arc discharge, and transitional state. Time-dependent simulations allowed for obtaining the dynamics of discharge formation. It is shown that after the breakdown, the cathode is heated by the discharge current for a time of tens of milliseconds, and then, transition to stable arc discharge with thermionic cathode takes place.