Joint grouting simulation is an important aspect of arch dam construction simulation. However, the current construction simulation model simplifies the temperature factors in joint grouting simulation, which leads to the difference between the simulation results and the actual construction schedule. Furthermore, the majority of existing temperature prediction research is based on deterministic point predictions, which cannot quantify the uncertainties of the prediction values. Thus, this study presents a real-time construction simulation method coupling a concrete temperature field interval prediction model to address these problems. First, a real-time construction simulation model is established. Secondly, this paper proposes a concrete temperature interval prediction method based on the hybrid-kernel relevance vector machine (HK-RVM) with the improved grasshopper optimization algorithm (IGOA). The hybrid-kernel method is adopted to ensure the prediction accuracy and generalization ability of the model. Additionally, the improved grasshopper optimization algorithm (IGOA), which utilizes the tent chaotic map and cosine adaptive method to improve the algorithm performance, is developed for the parameter optimization of HK-RVM. Thirdly, concept drift detection based on variable window technology is proposed to update the prediction model. Finally, an arch dam project in China is used as a case study, by which the superiority and applicability of the proposed method are proven.