To accommodate the nonlinear and dynamic nature of thermal elastic process, Grey System Theory (GST) is adopted. By using this theory, GM (2, 1) and GM (1, 4) models are constructed. Real cutting experiment on a turning machine is conducted to establish and validate the model performance in terms of generalization ability. The comparison indicates that GM (2, 1) and GM (1, 4) perform better than other static and dynamic models such as Back Propagation Neural Network (BP) and Auto-regression Moving Average (ARMA). In addition, each of the two proposed model has their own advantages and they can be applied in practice.