We introduce an approach to investigate thermal effects on the photoelectron spectra of small clusters. By combining first-principles molecular dynamics and a simplified scheme to account for final-state relaxation effects, we obtain averaged excitation spectra at finite temperature. We apply our approach to the case of Cu-7(-), in which two isomers are found very close in energy at T = 0 K. At T = 400 K, the isomer of D-5h symmetry transforms into one of C-3v symmetry. This behavior is in accord with the observed photoelectron spectra in which the predominant features can be associated with the C-3v isomer. The averaged spectrum at T = 400 K for this isomer suggests that the splitting observed in the peak at lowest excitation energies is a thermal effect.