The linear motor feed drive axis has the advantages of fast velocity, large acceleration, and short response time. However, the large heat generated by the primary coil easily causes thermal deformation of the external components and affects the positioning accuracy of the feed axis. To solve the problem, a thermal error modeling method for the direct-drive feed axis considering the multi-field coupling of “electromagnetic-thermal-fluid” is proposed. The electromagnetic, thermal, and flow fields of the direct-drive feed axis are analyzed, and the control equation of the temperature field is established under multi-field coupling. A simplified method for solving the control equation is proposed, which separates the equation into three stages, including heat generation, steady-state heat convection, and heat conduction. Then, the three stages are recoupled to obtain an explicit analytical model of the temperature field and the deformation field. The experimental results show that this model reveals the mechanism of the thermal error of direct-drive feed axes. It can accurately predict the thermal error, and automatically adjust the linear and nonlinear intervals, which is of great significance for improving the motion accuracy of direct-drive machine tools.