Several materials with mesoscopic characteristics (e.g. local defects or soft intergrain regions in granular materials) have been shown to share several nonclassical nonlinear features, which distinguish them from classical nonlinear media. Most striking among them is the log-time recovery of the material properties after they have been conditioned by the action of an external perturbation. A simple model based on the Local Interaction Simulation Approach is presented here for the description of the mesoscopic features as bonding regions among elastic elements. The implementation of the model is based on the application of a special bi-state protocol which, by the inclusion of thermally induced transitions between two basic states, allows to explain all the experimentally observed nonclassical nonlinear effects. We apply our model to analyze the effects of temperature changes on the elastic properties of materials by means of virtual resonant bar experiments, with a good qualitative agreement with the experimental results.