We studied experimentally and theoretically in detail a Si single-electron tunneling transistor which has a nanoscale floating dot gate stacked on a Coulomb island by a self-aligned process. At 4.2 K, this device exhibits drain current (Id) oscillations due to the Coulomb blockade effect besides the quantized threshold voltage (Vth) shifts with a hysteresis resulting from a single-electron tunneling between the channel and the floating dot gate. The periodicity of the Coulomb oscillation, the voltage separation (Delta V-w) between the adjacent two voltages where the Vth Shift occurs are consistent with those calculated from the geometrical consideration. The Coulomb oscillation disappeared at room temperature, however, the quantized V-th shifts and hysteresis curves, which are basic operations of single-electron memory, were observed up to room temperature. The fluctuation of electron number in the floating dot was theoretically analyzed at room temperature and we obtained consistent results with the experiments. The high on/off current ratio of the Coulomb oscillation combined with the quantized V-th shifts suggests that it might be possible to produce a memory with ultralow power consumption.