An efficient and accurate method for concrete thermal parameter inversion is essential to guarantee the reliable and prompt thermal analysis results of dams. Traditional inversion methods either suffer from low analysis efficiency or are limited in accuracy. Thus, this paper presents a method for multiple thermal parameter inversion based on an integrated surrogate model (ISM) and the Jaya algorithm. This method replaces finite element analysis with an ISM incorporating three machine learning algorithms, Kriging, support vector regression (SVR), and radial basis function (RBF), to describe the mapping relationship between thermal parameters and structure temperature responses. The input datasets for model training and testing are generated by a uniform design approach. Subsequently, a simple and efficient global optimization algorithm, Jaya, is used to identify the thermal parameters by minimizing the error between calculated and monitored temperatures. The effectiveness and practicality of this method are verified by applying monitored data of two strength grades of concrete in a dam. The verification results indicate that the proposed approach can obtain more accurate inversion results than the above individual models. Compared with these models, the inversion errors using ISM are reduced by 8.45%, 3.93% and 20.85%, respectively for C35 concrete, and by 6.53%, 23.82% and 44.43%, respectively for C40 concrete. Additionally, this approach maintains the powerful computational efficiency of surrogate-based optimization, and compared to the methods that directly invert using swarm intelligence algorithms, the analysis efficiency is improved by about 111.7 times.