In engineering practice, similar surface insulation measures are typically applied to different parts of mass concrete surfaces. However, this can lead to cracking at the edges of the concrete surface or the wastage of insulation materials. In comparison to flat surfaces, the edges of mass concrete structures dissipate heat more rapidly, leading to more pronounced stress concentration phenomena. Therefore, reinforced insulation measures are necessary. To reduce energy consumption and enhance overall insulation effectiveness, it is essential to study the specific insulation requirements of both the flat surfaces and edges of concrete separately and implement targeted surface insulation measures. Taking the bridge abutment planned for pouring in Nanjing City as the research object, this study established a finite element model to explore the effects of different ambient temperatures and different surface heat dissipation coefficients on the early-age temperature and stress fields of different parts of the abutment’s surface. Based on simulation results, reasonable heat dissipation coefficients that meet the requirements for crack prevention on both the structure’s plane and edges under different ambient temperatures were obtained. The results indicate that under the same conditions, the reasonable heat dissipation coefficient at the edges was smaller than that on the flat surfaces, indicating the need for stronger insulation measures at the edges. Finally, mathematical models correlating ambient temperature with reasonable heat dissipation coefficients for the structure’s plane and edges at these temperatures were established, with high data correlation and determination coefficients (R2) of 0.95 and 0.92. The mathematical models were validated, and the results from finite element calculations were found to be consistent with those from the mathematical models, validating the accuracy of the mathematical models. The conclusions drawn can provide references for the insulation of similar engineering concrete planes and edges.