Melt temperature distribution models for melting and plasticizing process of polymer materials were presented in vibration field induced extrusion, and the influences of process parameters such as die temperature, vibration amplitude and frequency on the melt temperature were investigated. Two kinds of ridge regression models based on the nonlinear transforms of polynomial and Gaussian RBF (PT-RR and GRBF-RR) were established to predict the melt temperature distribution with the nonlinear, non-isothermal properties and strong-coupling extrusion. The two models have fulfilled the nonlinear mapping and reconstruction of high-dimension feature space from multi-variable input samples, and obtained the coupling relations among multi-factor influences by the numerical simulation based on GRBF-RR. The simulation and experimental results show that the two models are valid and the correlation coefficients between the predicted values and that measured values are 0.994 0 and 1 for PT-RR and GRBF-RR, respectively. As the GRBF-RR can offer higher model precision, it was used to illuminate the influences of process parameters on the melt temperature distribution. Obtained results demonstrate that the model can provide a decision support for the quality control and process parameter optimization.