Temperature induced refractive index changes are an important aspect in today’s fiber amplifiers with high average power. For many processes, their time dependence is critical. Here, we analyze the impact of radial heat diffusion on the optical phase. We modulated the pump power in a 10 W amplifier and measured the frequency response of the optical phase. We compared the result with the calculated frequency response of the temperature in the fiber core, which shows the same characteristics. Additionally, we analyzed the influence of fiber parameters on the temperature dynamics.