Due to the large misfit (20%), Si grows in Stranski-Krastanov mode on SiC(0001) leading to the formation of Si islands with quantum-size (quantum dot) dimensions in the range of 2-6 nm in height and 10-25 nm in diameter after the transition from two-dimensional (2D) to 3D growth mode at coverages > 1.25 monolayers (ML). The growth mode transition and the post growth evolution of the system towards equilibrium surface conditions by dot formation was studied in real time at temperatures between 475 and 825 degrees C and coverages in the range of 2 ML by recording the RHEED intensities of both the specular beam and the (222)-Si-bulk spot. From that we analysed the temperature-dependent dynamic processes leading to dot formation. Above 625 degrees C, the formation of Si dots takes place within a sub-ML range above 1.25 ML. At these temperatures, the obtained activation energy of 0.6 eV for the dot growth indicates that surface diffusion is the dominant process. Below 625 degrees C, the occurrence of RHEED specular beam intensity oscillations indicates a 2D growth mode also at higher coverages. However, after the deposition was finished, the specular beam intensity decreased, and simultaneously, a 3D Si diffraction pattern occurred due to the formation of Si islands. The activation energy for the island growth process at these lower temperatures was determined to be much higher (2.1 eV), indicating a more complex process due to the mass transfer out of the 2D layer towards the Si islands.