This work presents an application of a linear Kalman filter to control the effects of thermal expansion in a recirculating ball screw of a computer numerical control (CNC) machine, impacting the final position accuracy of the machining tool. Through the Kalman filter, the system’s state ball screw position is estimated iteratively, allowing for real-time compensation of thermal variations, dilation, and positional inaccuracies on machining precision. The effectiveness of the proposed approach is demonstrated through experimental validation using a dataset comprising positional and temperatures measurements. The performance of the Kalman filter was evaluated through statistical analysis and for measurements taken during the heating cycle, the Y-axis exhibited R2 of 0.913 and \({\rm R}^{2}_{\rm adj}\) of 0.906, with an RMSE of 9.32 μm, indicating a good fit of the model to the data and acceptable precision of the estimates. For the X-axis under similar thermal conditions, higher values of R2 and R2adj were obtained with a lower RMSE confirming the high accuracy of the estimates and the method.