Usually the electron thermalization time scale in metals is in the range of femtoseconds to picoseconds (in gold you have a value of ~ 400 fs, for not so strong excitations). To study it you need excitation that are even faster, for example ultrashort laser pulses, which nowadays can be made as short as 3-4 fs at 800 nm wavelength.
The main (or faster) mechanism responsible for this thermalization, or relaxation, is electron-electron scattering. Electron-phonon scattering can also contribute, but on a tipically longer time-scale (few picoseconds).
The size of the object plays an important role when it affects the mean-free-path of the electrons inside the metal. This can happen in very small nanoparticles and in cluster, where the surface potential barriers changes the electron wavefunction. Otherwise what matters are the bulk properties of the metal, in primis its electron density. And the excitation strength, depending on which you can be in a "perturbative regime" (weak), or a non-perturbative one (strong).