In the contemporary era of machinery, the demand for highly precise machines exhibiting enhanced accuracy experiences a continuous upsurge in tandem with technological advancements. This has ignited fierce competition within the manufacturing sectors, driving their efforts toward the development of CNC machines with superior accuracy. The predominant factor adversely impacting machine precision is thermal-induced deformation. Multiple manufacturing sectors are actively engaged in research endeavors aimed at mitigating thermal distortion errors by formulating compensation models through the utilization of diverse machine learning and statistical techniques. This study focuses on a twin-spindle CNC turning machine, wherein real-time compensation methods are employed. Notably, machine learning methodologies, such as regression analysis, have been meticulously selected for implementation in this research. The resultant parameters are derived from the regression model and subsequently subjected to regularization techniques, enhancing the model’s accuracy. These refined parameters are then integrated into the CNC machine in the form of equations. The outcomes of the regularized regression exhibit significantly improved accuracy compared to conventional linear regression. Consequently, overall machine accuracy is markedly enhanced, leading to a 90% reduction in growth when compared to uncompensated results.