The ground state and finite-temperature properties of polarons are studied considering a two-site and a four-site Holstein model by exact diagonalization of the Hamiltonian. The kinetic energy, Drude weight, correlation functions involving charge and lattice deformations, and the specific heat have been evaluated as a function of electron–phonon (e–ph) coupling strength and temperature. The effects of site diagonal disorder on the above properties have been investigated. The disorder is found to suppress the kinetic energy and the Drude weight, and reduces the spatial extension of the polaron. Increasing temperature also reduces the kinetic energy, Drude weight and the polaron size when the e–ph interaction is weak or intermediate. For strong coupling the effect of temperature is small but opposite. For sufficiently strong coupling the kinetic energy arises mainly from the incoherent hopping processes owing to the motion of electrons within the polaron and is almost independent of the disorder strength. The specific heat shows a peak in the intermediate range of coupling, and the peak is suppressed in the presence of disorder. From the coherent and incoherent contributions to the kinetic energy, the temperature above which the incoherent part dominates is determined as a function of e–ph coupling strength.