Abstract: Based on the theory of envelope milling and homogeneous coordinate transformation, an analytical model of the influence of envelope milling gear thermal error on tooth profile error is established. The structure and machining characteristics of the machine tool are analyzed to determine the thermal characteristics of the machine tool lead screw. The thermal deformation of the lead screw is substituted into the machine tool error transfer matrix to obtain the tool helix deviation, and the relationship between the thermal expansion of the lead screw and the tooth profile error is studied. The results show that the axial thermal expansion of the lead screw will cause the deviation of the tool helical surface and the corresponding tooth profile error.