The optical parametric chirped-pulse amplifier (OPCPA) is one of the widely utilized amplifiers to boost ultra-short and ultra-intense pulses. The optical parametric fluorescence is the intrinsic quantum noise of OPCPA and the formed pedestal can degrade the temporal contrast of the output signal pulses greatly. Numerical simulation is adopted to study the evolution of the parametric fluorescence and its impact on the temporal contrast under various signal-to-pump duration ratios and various pump profiles. The results indicate that when the gain is fixed, the temporal contrast and the product of conversion efficiency and bandwidth increase firstly and then decrease with the increasing duration ratio. There is an optimal ratio to maximize the temporal contrast and the product simultaneously. When the ratio is lower than the optimal value, the temporal contrast decreases and the product increases with the increasing order of super-Gaussian pump profiles. The temporal contrast increases and the product decreases with the increasing order when the duration ratio is higher than the optimum.