We demonstrate Au-assisted vapor-solid-solid (VSS) growth of Ge nanowires (NWs) by molecular beam epitaxy (MBE) at 220 {deg}C, which is compatible with the temperature window for Si-based integrated circuit. Low temperature grown Ge NWs hold a smaller size, similar uniformity and better fit with Au tips in diameter, in contrast to Ge NWs grown at around or above the eutectic temperature of Au-Ge alloy in the vapor-liquid-solid (VLS) growth. Three growth orientations were observed on Ge (110) by the VSS growth at 220 {deg}C, differing from only one growth direction of Ge NWs by the VLS growth at a high temperature. The evolution of NWs dimension and morphology from the VLS growth to the VSS growth is qualitatively explained via analyzing the mechanism of the two growth modes.