Heterodyne interferometers suffer from thermal drift of optics (TDO), which may introduce error even up to several micrometers. In this paper, we propose a symmetric heterodyne interferometer with spatially separated beams, which realizes completely balanced optical paths between probe and reference beams and simultaneously avoids the optical mixing, and thereby is theoretically capable of eliminating TDO and the periodic nonlinearity (PNL). To validate the performance of the proposed interferometer, first a special experimental setup is constructed, with which the TDO test can be conducted in vacuum, and the result shows that a thermal coefficient of 1.2 nm/°C is achieved. Next, the PNL of the proposed interferometer is measured by both the frequency domain method and the phase quadrature method, which demonstrates an undetectable PNL at a noise level of 13 pm.