To meet the demands for high-temperature performance and lightweight materials in aerospace engineering, the Au-Ni solder is often utilized for joining dissimilar materials, such as Ti3Al-based alloys and Ni-based high-temperature alloys. However, the interaction between Ti and Ni can lead to the formation of brittle phases, like Ti2Ni, TiNi, and TiNi3, which diminish the mechanical properties of the joint and increase the risk of crack formation during the welding process. Cu doping has been shown to enhance the mechanical properties and high-temperature stability of the Au-Ni brazed joint's central area. Due to the difficulty in accurately controlling the solid solution content of Cu in the Au-Ni alloy, along with the high cost of Au, traditional experimental trial-and-error methods are insufficient for the development of Au-based solders. In this study, first principles calculations based on density functional theory were employed to analyze the effect of Cu content on the stability of the Au-2.0Ni-xCu (x = 0, 0.25, 0.5, 0.75, 1.0, 1.25 wt%) alloy phase structure. The thermal properties of the alloy were determined using Gibbs software fitting. The results indicate that the Au-2.0Ni-0.25Cu alloy exhibits the highest plastic toughness (B/G = 5.601, ν = 0.416, Cauchy pressure = 73.676 GPa) and a hardness of 1.17 GPa, which is 80% higher than that of Au-2.0Ni. This alloy balances excellent strength and plastic toughness, meeting the mechanical performance requirements of brazed joints. The constant pressure specific heat capacity (Cp) of the Au-2.0Ni-xCu alloy is higher than that of Au-2.0Ni and increases with Cu content. At 1000 K, the Cp of the Au-2.0Ni-0.25Cu alloy is 35.606 J·mol-1·K-1, which is 5.88% higher than that of Au-2.0Ni. The higher Cp contributes to enhanced high-temperature stability. Moreover, the linear expansion coefficient (CTE) of the Au-2.0Ni-0.25Cu alloy at 1000 K is 8.76 × 10-5·K-1, only 0.68% higher than Au-2.0Ni. The lower CTE helps to reduce the risk of solder damage caused by thermal stress. Therefore, the Au-2.0Ni-0.25Cu alloy is more suitable for brazing applications in high-temperature environments due to its excellent mechanical properties and thermal stability. This study provides a theoretical basis for the performance optimization and engineering application of the Au-2.0Ni-xCu alloy as a gold-based solder.