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Understanding how light interacts with matter at the nanoscale is pivotal if one is to properly engineer nano-antennas, filters and other devices whose geometrical features approach atomic size. We report experimental results on second and third harmonic generation from 20 nm- and 70 nm-thick gold layers, for TE- and TM-polarized incident light pulses. We discuss the relative roles that bound electrons and an intensity dependent free electron density (hot electrons) play in third harmonic generation. While planar structures are generally the simplest to fabricate, metal layers that are only a few nanometers thick and partially transparent are almost never studied. Yet, transmission offers an additional reference point to compare experimental measurements with theoretical models. Our experimental results are explained well within the context of the microscopic hydrodynamic model that we employ to simulate second and third harmonic conversion efficiencies. Using our experimental observations we estimate |¿(3)1064¿¿|˜10-18 (m/V)2, triggered mostly by hot electrons., Postprint (published version)