We present an ab initio molecular dynamics study of the structure and dynamics of a close-packed monolayer of Pb on the Ge(111) surface, with coverage FTHETA=4/3, at different temperatures. The room-temperature (√3 × √3 ) structure is characterized by large in-plane fluctuations of the Pb adatoms, and agrees well with recent x-ray standing wave data. At T∼800 K we observe a (1×1) disordered structure showing in-plane diffusion of the Pb atoms. Disordering is confined to the plane of the overlayer. A strong correlation with the solid Ge substrate is present, leading to preferential residence sites and diffusion paths of the Pb atoms on the surface. The calculated local density of states for the high-temperature phase is found to agree with recent scanning tunnel microscope observations, which show a simply Pb-terminated (1×1) surface with an apparent coverage FTHETA=1.