<p>Thermal errors have become the main factor affecting the machine tool accuracy. Statistical prediction and compensation models are commonly established based on the measured temperature data to reduce thermal errors. Current literature typically focuses on first selecting temperature-sensitive points (TSPs) to reduce multicollinearity and then building thermal error models for CNC machines. Thus, this two-step approach loses useful information after the variable selection and prevents thermal error models from using this lost information. In addition, there are few approaches that can simultaneously reduce multicollinearity through variable selection and model thermal errors in one single step. Therefore, to fill the research gap, a one-shot thermal error modeling and prediction approach is proposed based on the individually penalized ridge regression (IPRR). Specifically, the traditional ridge regression method, which intrinsically fails to select TSPs, is adopted and modified by setting up individually penalized ridge parameters for each variable, thereby achieving both variable selection and thermal error modeling simultaneously. Then, the proposed IPRR algorithm is compared using the experimental data with the existing methods. The comparison results show that the IPRR algorithm can significantly improve the prediction accuracy by 10% and robustness by 40% on thermal errors. Finally, the thermal error compensation experiments are conducted on the experimental object to show the practicability of the IPRR algorithm.</p>