An approximate method for electron band-structure calculations on structurally disordered materials is presented. Our approach is essentially a linear-muffin-tin-orbital calculation in which the structure matrix of a disordered supercell is reduced to the size of one atom per unit cell through an averaging procedure. Potential fluctuations are included by treating Madelung shifts as perturbations. A lattice of atoms with uncorrelated displacements is studied, and we show how total-energy results should be compared with experimental thermodynamic information. In particular, we expect an almost quasiharmonic behavior for calculated thermodynamic properties. We use our method to calculate Debye temperatures FTHETAD, for all 4d transition metals from Zr to Pd in the bcc, fcc, and hcp structures, and we discuss the physical reasons for variations in FTHETAD. Anharmonic effects are studied by determining thermal expansions and bulk moduli as functions of temperature. Being an ab initio calculation, our results are in very good agreement with experiment. Electronic energy spectra at finite temperatures are presented and we comment on similarities with previous results on liquid transition metals.