The capability to tune the linear and nonlinear optical response of plasmonic nanoarrays is of great interest for the realization of solid-state plasmonic nanodevices with application in many different fields in nanophotonics. In the present work we demonstrated the possibility to tailor, in a controlled way, the morphological properties of gold nanoprism arrays fabricated by nanosphere lithography, by performing thermal annealing treatments in air, preserving their bidimensional ordered arrangement. This allows to engineer the linear optical properties of the samples, finely tuning the spectral position and amplitude of their surface plasmon resonance peak. Moreover, we demonstrated that the fine control of the nanostructures' morphology provides a way to get the continuous modulation of the nonlinear optical parameters (nonlinear refractive index and nonlinear absorption coefficient) of the nanoarray. The experimental findings have been supported by finite elements method electrodynamic simulations, which provided a very good agreement.