Single Crystal Fiber (SCF) laser is widely applied into scientific research and engineering, owing to its superior thermal management, compact mechanical structure and high power output. In this paper, the temperature field of an Nd:YAG SCF laser related to thermal effect produced by pump laser is presented. By solving the heat conduction equation with the analytical method, the thermal model of Nd:YAG SCF is studied. The temperature distribution of Nd:YAG SCF producing a 946 nm laser by an 808 nm pumping light with power of 86 W is obtained. Results show that the maximum temperature rise at the incident end face of SCF is 30.98℃, obviously lower than that of an Nd:YAG crystal of 94.37℃ under the same conditions. Besides, compared with a temperature rise of 19℃ in SCF obtained by Finite Element Analysis(FEA), temperature rise calculated by analytical method are closer to the experimentally measured value of 31℃. This indicates that the analytical method is more realistic and accurate in describing the temperature field of Nd:YAG SCF. The temperature characteristics of the SCF and the influence of some important parameters are also studied. One of the key factors is the absorption coefficient of the SCF, which has an approximately linear relationship with its temperature rise. Another factor is the core radius of the SCF, which is proportional in value to the rise in temperature. The temperature rise increases with core radius, while decreasing with beam radius of 808 nm pump laser. The root mean square is applied to precisely describe the temperature affected by these parameters. According to the data analysis, uniform distribution in the temperature field can be realized by appropriately selecting the above parameters. The research can be a reference for controlling the thermal effect of single crystal fiber lasers and improving its performance.