Abstract A theoretical approach to the electronic structure of solids at finite temperature has been developed on the basis of the adiabatic approximation. For any given temperature, correlated ion core displacement configurations on a large cluster are determined, which are consistent with experimental phonon dispersion relations. The electron Bloch spectral function, i.e. a generalized band structure, and photoemission intensities are obtained by a tight-binding recursion method for each configuration followed by a configurational average. Calculations for the 3 d-band region of Cu yield the vibration-induced hole lifetime broadening (typically about 0.35 eV at 900 K) and real energy shifts (up to ±0.1 eV). Due to a compensation by thermal lattice dilation, the d-band width changes only marginally with T. Comparison with experimental photoemission data from Cu(1 1 0) shows good agreement for the temperature dependence of peak height, line shape and energy shift.