The electronic dynamics of gold nanocrystals, passivated by a monolayer of alkylthiol(ate) groups, were studied by transient spectroscopy after excitation with subpicosecond laser pulses. Three solution-phase gold samples with average particle size of 1.9, 2.6, and 3.2 nm with size distribution less than 10% were used. The photoexcitation in the intraband (surface plasmon region) leads to the heating of the conduction electron gas and its subsequent thermalization through electron-electron and electron-phonon interaction. The results are analyzed in terms of the contribution of the equilibrated "hot" electrons to the surface plasmon resonance of gold. A different spectral response was observed for different sizes of gold nanoparticles. The results were compared to the dynamics of the large (30 nm diameter) gold nanocrystals colloidal solution. The size-dependent spectral changes are attributed to the reduction of the density of states for small nanoparticles. The observed variation in the kinetics of the cooling process in gold nanoparticles with changing the laser intensity is attributed to the temperature dependence of the heat capacity of the electron gas.