We investigate the thermoelectric energy conversion efficiency of Si and Ge nanowires, and in particular, that of Si/Ge core-shell nanowires. We show how the presence of a thin Ge shell on a Si core nanowire increases the overall figure of merit. We find the optimal thickness of the Ge shell to provide the largest figure of merit for the devices. We also consider Ge core/Si shell nanowires, and show that an optimal thickness of the Si shell does not exist, since the figure of merit is a monotonically decreasing function of the radius of the nanowire. Finally, we verify the empirical law relating the electron energy gap to the optimal working temperature that maximizes the efficiency of the device.