The cooling dynamics of individual gold nanodisks synthesized using colloidal chemistry and deposited on solid substrates with different compositions and thicknesses were investigated using optical time-resolved spectroscopy and finite-element modeling. Experiments demonstrate a strong substrate-dependence of these cooling dynamics, which require the combination of heat transfer at the nanodisk/substrate interface and heat diffusion in the substrate. In the case of nanodisks deposited on a thick sapphire substrate, the dynamics are found to be mostly limited by the thermal resistance of the gold/sapphire interface, for which a value similar to that obtained in the context of previous experiments on sapphire-supported single gold nanodisks produced by electron beam lithography is deduced. In contrast, the cooling dynamics of nanodisks supported by nanometric silica and silicon nitride membranes are much slower and largely affected by heat diffusion in the membranes, whose efficiency is strongly reduced as compared to the thick sapphire case.