The thermal error of machine tool spindle system has become an important factor affecting machining accuracy. Measurement experiments of a 3-axis vertical milling machine spindle system were conducted to assess temperature fields and thermal errors. The fuzzy clustering and gray correlation algorithms were adopted to cluster the temperature measuring points and identify the temperature-sensitive points. Based on the adaptive chaos particle swarm optimization algorithm, thermal error models were established in the axial and radial directions for the spindle system, and the compensation effects were evaluated by the workpiece machining accuracy. The results showed that the number of temperature measuring points was reduced from 12 to 6. The residual range of measured and predicted thermal error values in the axial direction was 6.17-4.19 μm, and the modeling accuracy was 95.53%. The radial residual ranges were − 2.75-3.05 μm and − 2.10-2.15 μm, and the modeling accuracies were 90.74% and 91.10%, respectively. The model compensation effect was demonstrated remarkably in the verification experiments. The thermal error models showed high prediction precision, could improve machining accuracy and had strong engineering application value.

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