To address the issues of large finite element computation volume and strong nonlinear response relationships in special thread connections under multi-parameter, multi-load state conditions, a two-dimensional axisymmetric parametric finite element model was established. Latin hypercube sampling was employed to generate combinations of radial interference, load flank angle, taper percentage, and friction coefficient, and Abaqus script interface was invoked via Python to automate composite load application and response data extraction. With four model-level parameters, temperature, axial load, internal/external pressure, and contact area as inputs, XGBoost regression models were independently established for effective contact length, maximum contact pressure, maximum Mises stress, and maximum equivalent plastic strain. A data partitioning method based on model ID grouping was adopted to evaluate the models' prediction capability for unseen parameter combinations. The results show that the coefficient of determination (R²) of the four models on the independent test set were 0.999944, 0.812840, 0.780395, and 0.983697, respectively, and the cross-validation prediction results on the training set were generally consistent with the independent test results. Complete load spectrum analysis reveals that the extrema of different sealing and structural responses correspond to different load states, and a single loading condition is insufficient to fully characterize the connection service response. SHAP analysis indicates that taper percentage is the machining parameter with the highest contribution across all four responses, followed by radial interference in its influence on maximum contact pressure and maximum Mises stress. The established models can be used for state-augmented prediction of existing finite element databases and provide a basis for control of special thread machining parameters and dimensional inspection.