A higher-order beam model based on the asymptotic expansion method was suggested by Ferradi et al.. Introducing new degrees of freedom specific to the applied loads into the kinematics of the beam, this model yields fast and accurate results. The present paper focuses on the extension of this model to the case of arbitrary eigenstrains expressed in a separate form between the longitudinal coordinate and the in-section coordinates. The asymptotic expansion procedure is recalled and the derivation of a higher-order beam model performed. The beam model is interpolated with NURBS. The case of a bridge deck heated on a localized area is studied. A second case study of a prestressed cantilever beam is then investigated. The results of the higher-order beam model are compared to a 3D solution in each example. The performances of the beam model appears to be accurate and very time-efficient.