  We present a theory for the electron-temperature dependence $T_{el}$ of
optical second harmonic generation (SHG). Such an analysis is required to study
the dynamics of metallic systems with many hot electrons not at equilibrium
with the lattice. Using a tight-binding theory for the nonlinear susceptibility
\cwtel and the Fresnel coefficients we present results for the SHG intensity
\iwtel for a Cu monolayer. In the case of linear optical response we find that
the intensity will decrease monotonously for increasing $T_{el}$. In agreement
with experiment we find a frequency range where \iwtel may be enhanced or
reduced depending on electron temperature. Note, \cwtel rather than the Fresnel
coefficients determines essentially the temperature dependence. Our theory
yields also that SHG probes effects due to hot electrons more sensitively than
linear optics. We also discuss the $T_{el}$-dependence of SHG for Au and Ag.
