There are many kinds of permanent-magnet (PM) motors, which are widely used in modern industry, but the problem of temperature rise is likely to affect the operation performance and even the life of the motor. The semiclosed structure of the PM spherical motor (PMSM) tends to increase the temperature when it works, so the thermal analysis of the PMSM is considered necessary. Based on double Fourier series decomposition, this paper establishes a three-dimensional (3-D) analytical model of PM eddy current loss in the PMSM, which considers the effect of time and space harmonics. Meanwhile, the heat sources such as hysteresis loss and copper loss are discussed. With those heat sources, a 3-D equivalent thermal network model is established. The thermal resistances are calculated. By applying the thermal network model, the influence of different speed and load on temperature rise is analyzed, and a steady-state thermal analysis of the motor is performed by using finite element analysis. The structure of stator is improved and good heat dissipation effect is achieved. This paper provides the theoretical basis for the design of ventilation and cooling system of the PMSM.