During the coiling process of a hot-rolled strip, with the increasing layers the temperature and stress distribution inside the coil constantly change and interact with each other. Due to the contact with the sleeve and the transition of the heat exchange state, it is inaccurate to consider the temperature of the whole coil as the coiling temperature set by the process requirement. Meanwhile, due to the periodic interlayer contact in the radial direction, the relation between stress and deformation is nonlinear. For the coiling process, it is difficult to consider the above factors using conventional methods. Therefore, an incremental model has been established to couple the temperature and stress of the coil. In order to obtain the mechanical properties of the strip and radial elastic modulus of the coil, tensile tests and laminated compression experiments are conducted at different temperatures. The effects of changes in strip thickness, coiling tension, and initial temperature of the sleeve on the stress and the temperature inside the coil are studied. Finally, by comparing the model results with measurements and analytical solutions, the effectiveness of the incremental coupled model is verified and the errors caused by the analytical method are analyzed.