Thermal error of spindle of the CNC machine tool is one of the main factors affecting machining accuracy of the machine tool. In order to improve accuracy of the thermal error measurement and reduce the measurement technology requirements, a thermal error information separation method of machine tool based on the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and empirical wavelet transform (EWT) is proposed. Firstly, the original signal is decomposed using the ICEEMDAN algorithm, the obtained low-frequency modal components are reconstructed and used as input of the EWT algorithm for decomposition, and the discrete coefficients are used to evaluate the decomposition effect of each iteration of the EWT algorithm. Secondly, accuracy of the ICEEMDAN–EWT algorithm was verified by decomposing a set of simulated signals, and root mean square error (RMSE) of the algorithm was reduced by 5.2% compared with the ICEEMDAN algorithm. Finally, experiments were conducted on a CKA6 163A machine tool to identify thermal errors using the five-point method, comparing the ICEEMDAN–EWT separation algorithm with the Fourier transform (FFT) algorithm. The experimental results show that compared with the FFT algorithm, the Pearson correlation of the five thermal deformation signals and machine tool temperature obtained by ICEEMDAN–EWT algorithm is improved by 3.8% and the Spearman correlation improved by 6.6%, indicating the proposed method is with higher accuracy.