Direct-current micro-scale gas discharges have attracted much attention of the researchers due to the interesting plasma physics involved in the discharges and their bright aspects in different fields. In previous studies, the secondary electron emission and field emission processes have been studied by many authors, however, the thermionic emission with a heated electrode surface is scarcely investigated, which may influence the characteristics of the micro-discharge. In this paper, a one-dimensional implicit particle-in-cell Monte Carlo collision method is employed to study the kinetic behaviors of the direct-current micro-discharges using argon as the plasma forming gas at atmospheric pressure, in which the thermionic emission from the heated cathode is considered. The species number densities, breakdown voltage, the spatially averaged electron energy probability function and electric field with different electrode gap spacings are predicted, and the influences of the thermionic emission process on the features of the micro-discharges are revealed.