<p>Servo presses offer improved flexibility in product design together with higher process efficiency; however, machining tolerances induced by thermal deformation and the associated risk of mold damage must be carefully controlled in high-precision manufacturing. This study proposes a practical method for estimating clamping position errors by measuring temperatures at a set of critical locations on the press. Finite element analysis (FEA) is first employed to obtain the transient thermal deformation behavior of key structural components. Based on these data, a detrending time-series approach and a newly defined index, the Energy Influence Depth (EID), are used to quantify the depth to which thermal energy is transmitted within a specified region. A compact neural network model is then trained to predict the clamping position error under thermal loading in the ideal (simulation-based) case, achieving test accuracies of 96% and 97% for the two sides of the moving head, thereby indirectly validating the effectiveness of the proposed EID index. Subsequently, thermal-deformation experiments are conducted on a scaled physical press, and the same model development strategy is applied to construct an experiment-based prediction model using measured temperatures and EID values as inputs. The experimental model attains test normalized root-mean-square errors (NRMSE) of 0.10 and 0.07 for the left and right sides, respectively, and reproduces the overall trend of the measured deformation, although overestimation or underestimation may occur in some cases, likely due to limited training data. Overall, combining the proposed Energy Influence Depth with a lightweight neural network yields a feasible and practically deployable approach for predicting bed position error in servo presses.</p>