Ge–Si core–shell nanowires with surface disorder are shown to be very promising candidates for thermoelectric applications. In atomistic calculations we find that surface roughness decreases the phonon thermal conductance significantly. On the contrary, the hole states are confined to the Ge core and are thereby shielded from the surface disorder, resulting in large electronic conductance values even in the presence of surface disorder. This decoupling of the electronic and phonon transport is very favorable for thermoelectric purposes, giving rise to promising room temperature figure of merits ZT > 2. It is also found that the Ge–Si core–shell wires perform better than pure Si nanowires.