The K/Si(111):B root 3 x root 3 surface, with one K atom per root 3 x root 3 unit cell, is considered a prototypical case of a surface Mott phase at room temperature. Our Density Functional Theory (DFT) Molecular Dynamics (MD) and free energy calculations show, however, a 2 root 3 x root 3 Charge Density Wave (CDW) ground state. Our analysis shows that at room temperature the K atoms easily diffuse along the lines of a honeycomb network on the surface and that the root 3 x root 3 phase appears as the result of the dynamical fluctuations between degenerate CDW states. DFT-MD free energy calculations also show a 2 root 3 x root 3 <--> root 3 x root 3 transition temperature below 90 K. The competing electron-electron and electron-phonon interactions at low temperature are also analyzed; using DFT calculations, we find that the electron-phonon negative-U * is larger than the electron-electron Hubbard U, indicating that the CDW survives at very low temperature.