Rolling resistance (RR) is key research content for developing low-carbon energy-saving tires, and the resultant change in the tire temperature field exerts a crucial impact on tire performance. Currently, there is no accurate and systematic analysis method for solving the steady-state temperature field (SSTF) and RR of tires with complex patterns and non-pneumatic tires (NPTs), which are characterized by discontinuous structure in the circumferential direction. A solution strategy that entails SSTF and RR based on explicit transient rolling analysis and thermal-mechanical coupling is proposed and its accuracy is verified using the SSTF test pertaining to the low-speed and low-load capacity non-pneumatic tire (LSL-tire), which exhibits a 7.56% and 6.94% average temperature deviation for the outer surface center of the tread and for the outer surface center of spokes, respectively. Uniaxial tensile mechanical property tests and dynamic mechanical analysis (DMA) of the utilized rubber and polyurethane (PU) materials were conducted, and their specific heat capacity, thermal conductivity, and density were tested. Based on three-dimensional nonlinear finite element simulation and considering the characteristics pertaining to the loss factor of viscoelastic materials changing with temperature, the SSTF and RR of the LSL-tire under different loads and velocities were analyzed. The results indicate that the influence of load and speed on the SSTF of LSL-tire is quite significant, whereas the influence of speed on the RR is not apparent. For all conditions, the highest steady-state temperature points of the tread are located in its center, and in the spokes they are located in the joint between spokes and the outer ring; the spokes contribute the most to the RR, followed by the tread.