Master oscillator power amplifier (MOPA) is a common configuration in fiber lasers to obtain high power output. Amplified spontaneous emission (ASE) is amplified stage by stage by MOPA, which may result in damage to the fiber amplifier. In the experiment of high-power fiber amplifier, thermal effect is one of the most critical issues. High temperature from significant thermal effect would restrict the further improvement of laser power and cause the fiber to damage. In most of the experiments, the gain fibers are broken usually at the place 10-50 cm away from the fused point of the pump injection end. To better understand in physics the highest temperature and the position of the burning point, we study the ASE and temperature characteristics by using the rate equation model of fiber laser and the thermal conduction model of gain fiber. We analyze the influences of seed power, pump power and pump absorption on Yb-doped double-cladding fiber amplifier. The results show that when magnification is relatively high and ASE is serious, the highest temperature point of the fiber amplifier is not at the fused point of the pump injection end but at the place 10-50 cm away from the fused point, which consists well with the experimental result. For studying the ASE suppression and the temperature control of the hottest point, we compare the three parameters in the 915 nm pumped case with those in the 975 nm pumped case, these being power ratio of ASE to the output laser, hottest location along the fiber, and the ratio of the temperature difference between the highest temperature and fusion point temperature to the latter one. It is concluded that the optimal parameters for the 915 nm pumped case are seed power larger than 7 W, pump power less than 1250 W, and pump absorption less than 20 dB. As to the 975 nm pumped case, it is suggested that the seed power should be not less than 8 W with an appropriate pump power. The research also implies that a better performance of fiber amplifier is pumped by 975 nm under the same condition. To prevent the local internal hot point from forming and the potential burnout risk from happening, the magnification of fiber amplifier needs to be set below 50-fold. In conclusion, this work presents a suggestion for optimizing the fiber amplifier design through using appropriate seed power, pump power, pump absorption, magnification and pump wavelength.