Fundamental mode orthogonal fluxgate (FM-OFG) adopting the bias switching technique is a promising compact and low-noise magnetometer for precise DC and low frequency magnetic field measurement. Yet, its output offset stability is insufficient for measurements in the environment with large temperature variations. In this research we have experimentally investigated the cause of the residual offset and its drift found in the bias-switched FM-OFG. Then we proposed a simple and effective method to drastically improve the sensor temperature characteristics of the FM-OFG in a practical feedback design with analog circuitry. Ideally, the induced voltages arisen by the uniaxial anisotropy of an amorphous wire core become symmetrical under flipped excitation polarities, and thus they are canceled by averaging. However, it was revealed that there was certain imbalance between them due to the asymmetry in wire’s magnetic properties, producing remnant component in the final output. The proposed method achieves equilibration of the imbalance component within the demodulation process of the induced voltages to minimize the residual offset and its drift in the final, averaged output. The method was verified by the experiment, and the offset stability of 0.013 nT/°C within the temperature range from −60°C to +70°C was achieved with good repeatability.