We have performed extensive numerical simulations to study the effect of the size of pinning centers on the critical current density of driven vortex lattices interacting with square periodic arrays of pinning sites. The pinning centers considered here have radii larger than the superconducting coherence length of the vortices. These simulations have been carried out at different temperatures and for several values of pinning strengths. We have solved the overdamped equation of vortex motion taking into account the vortex–vortex repulsion interaction, the attractive vortex–pinning interaction, the thermal force, and the driving Lorentz force. We have found that, while the critical current density increases with pinning size at high-temperatures, it is almost independent of pinning size at low-temperatures. We have also found that increasing the size of the pinning centers suppresses the rate at which the critical current density decreases with temperature for all values of pinning strength.