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It is essential to develop the predictive model of thermal error for multilink high-speed precision press system (MHSPPS) in order to construct its compensation on the slider's position accuracy at the bottom dead point (BDP). In this work, based on the principal factor strategy and the clustering methodology, the locations of thermal sensitive points (TSPs) on the MHSPPS are determined and the corresponding temperature is taken as the feed in parameter of the thermal error model (TEM). An improved adaptive genetic algorithm (IAGA) incorporated with a back-propagation neural network (BPNN) is then presented so as to simulate and predict the thermal error of MHSPPS through the collected temperature of TSPs. Compared with the experimental results, accuracy of the predictive model forward goes beyond that of the traditional TEMs, such as multiple linear regression (MLR), genetic algorithm with BPNN (GA-BPNN), and particle swarm optimization with BPNN (PSO-BPNN) models, which proves effectiveness of the proposed model. In order to implement the compensation experiment, a novel adjustment mechanism of slider's BDP position for MHSPPS is designed and the compensation algorithm with online correction based on the IAGA-BPNN model is also proposed. Test results indicate that the maximum errors and the RMS errors of the slider's BDP position after compensation with online correction based on the proposed IAGA-BPNN model can be reduced to 93.33% and 98.75%, respectively, which verifies the authenticity of thermal error compensation based on the IAGA-BPNN model and online correction algorithm. [ABSTRACT FROM AUTHOR]