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• A direct equivalent heat release model for concrete considering temperature history. • An integral method for precisely calculation in large time step interval. • An iterative method for precisely calculating hydration temperature rise. • The proposed method exhibits high calculation precision and efficiency. Current hydration heat release rate algorithms that consider the temperature history are based on the Arrhenius law and other hypothetical conditions. Nevertheless, reported research results have shown controversy regarding the values of Arrhenius law and other model parameters, potentially introducing errors in calculated results. Some studies have shown that adiabatic temperature rises at different placement temperatures can be expressed by a mathematical expression; thus, this study establishes a relational model for the hydration temperature rise rate of concrete structures under any temperature history. This study uses the hydration temperature rise rate of the adiabatic temperature rise test under equivalent conditions to directly obtain the hydration temperature rise rate for any temperature history. Except for special cases, the proposed algorithm does not rely on the Arrhenius law and other hypothetical conditions, thus avoiding errors caused by the associated assumptions. Additionally, this study utilizes an integration method to solve a problem in which a small calculation time step is required to guarantee the accuracy of the solution under the conventional finite element framework. Furthermore, an iterative algorithm is proposed to solve the problem in which the temperature at the end of the calculation time step must be used when the temperature history is considered. Examples show that the proposed method exhibits a high calculation precision and improves efficiency; and the maximum temperature difference between the calculated and measured values is only 0.085 °C. [ABSTRACT FROM AUTHOR]