Understanding of the melting temperature of nanostructures is beneficial to exploit phase transitions and their applications at elevated temperatures. The melting temperature of nanostructured materials depends on particle size, shape and dimensionality and has been well established both experimentally and theoretically. The large surface-to-volume ratio is the key for the low melting temperature of nanostructured materials. The melting temperature of almost free nanoparticles decreases with decreasing size although there are anomalies for some cases. Superheating has been reported for some embedded nanoparticles. Local maxima and minima in the melting temperature have been reported for particles with fewer atoms. Another quantity that is influenced by large surface-to-volume ratio and related to the thermal stability, is the vapour pressure. The vapour pressure of nanoparticles is shown to be enhanced for smaller particles. In this article, we have discussed the anomaly in thermal stability of nanostructured materials.