Using finite-temperature molecular dynamic simulations, we study the lower-frequency voltage noise in two-dimensional random-pinning-vortex lattices. We calculate the voltage noise spectrum of the vortex motion, and obtain the broadband noise (BBN) as a function of the driving current, pinning strength, and temperature. It is found that BBN increases with the pinning strength, and decreases with increasing temperature. These results are consistent with experiments and may be understood in terms of the microscopic dynamics of vortex motion.