The local heat and wear generated due to friction in a precision motion stage in electronic packaging equipment have a significant impact on its positioning precision. In this paper, we studied the temperature changes over time and the wear of a linear rolling guide (LRG) in a rigid–flexible coupling motion stage (RFCMS), both analytically and experimentally, and we proposed an evaluation method for LRG wear in an RFCMS. According to Fourier’s law and the law of conservation of energy, the differential equation of heat conduction for the LRG and the thermal boundary conditions were established. Steady-state and transient thermal simulations were carried out using ANSYS Workbench to predict the temperature increase in the LRG due to friction. Finally, a test apparatus was built to demonstrate that an RFCMS reduced the operating temperature of the LRG, which also reduced the wear on the contact surface. Through response surface methodology, the levels of the influence of different flexure hinge thicknesses, strokes, velocities, and accelerations on the temperature change rate (TCR) of the LRG were obtained, as well as the approximate regression equation of four variables of the TCR. This provided a new research method for precision maintenance, life design, and operational parameter selection for high-precision motion stages.