The DC-driven atmospheric-pressure microplasma is generated in a helium gas flowing through the metal tube cathode and is brought into contact with the surface of the water with the immersed Pt anode. By adjusting the gas flow, discharge current and gap distance, self-organized patterns are observed and varied sequentially from the homogeneous spot to the ring-like shape, distinct spot shape and the gearwheel shape on the water surface. The electrode temperature is measured and the gas temperature of the plasma discharge is calculated through the numerical fitting of the second positive system of the spectrum of N2 molecules. It is shown that the pattern transition is related to the electrode and gas temperatures of the plasma. Moreover, specific discretization features of the patterns are shown to appear at certain gas temperatures.