In this letter, we study the asymmetric increase of write error rate (WER) as the write voltage is elevated in spin-orbit-torque (SOT) magnetic tunnel junctions (MTJs) with perpendicular magnetic anisotropy. Besides the decrease of the free layer’s (FL) coercive field rendering the FL more vulnerable to the influence of offset field from synthetic antiferromagnets (SAFs), we observe, that during the write process, the temperature rise caused by the self-heating effect also modifies the magnetic properties of SAF layers in MTJ stacks. Through the measurement and analysis of two device types with different SAF designs, the amplitude and direction of the offset field show different temperature dependence, which determines an opposite preferentially stable state for the FL, and hence the anomalously high WER. Macrospin simulations of WER incorporating self-heating effect and temperature-dependent magnetic properties in both FL and SAF reproduce well the experimental observations. These findings offer novel insights into the role of the offset field and its temperature dependence in optimizing WER performance in SOT-MTJ devices.