We reconsider the question of thermal radiation from accelerated mirrors in the model of Fulling and Davies, with the assumption that the mirror moves inertially after a finite acceleration time t_a. We obtain the Planck distribution by calculating the emitted spectrum as lim_{t_a∞} N_ω(t_a)/t_a, where N_ω(t_a) is the number of quanta produced in the ω mode on the trajectory with acceleration time t_a.