For a solid with free surfaces, the melting always starts from its surfaces, which are easier to melt as the atoms there vibrate more strongly than the bulk. If the surfaces are covered by some other materials that are harder to melt than the solid itself, it can then be superheated. This has been verified by experiments. 

In fact, there is. Water, for example, can be supercooled down to −48 °C. From organics, glycerol is the most famous example of the easily supercooled compounds. Its melting point is 17.8 °C, but it almost never crystallizes at this temperature and it is possible to keep it liquid below −80 °C.

So what is the cause of this?

Are there know examples of superheated organic crystals?

I am thinking about the Born hypothesis/theory of melting... If crystals can be superheated, then they should have a finite bulk/shear modulus above the melting point temperature.

I found this review on the topic, probably it will be useful: http://dx.doi.org/10.1016/j.tca.2006.11.015

Dear Jonas,

Freezing hysteresis is defined as the difference between the equilibrium melting point and the non-equilibrium freezing point, which is the temperature at which a crystal that is not growing in a super cooled solution suddenly grows rapidly (bursts). Although it has been more than 40 years since AFPs were discovered in Antarctic fish, how these proteins function at the ice-water interface remains a matter of debate. There is no consensus in the AFP field in regards to whether AFPs bind reversibly or irreversibly to ice surfaces. The adsorption inhibition model, which suggests that AFPs bind to ice surfaces irreversibly The adsorption inhibition model indicates that ice will grow in the gaps where no AFPs are located. This process increases the curvature of the ice surface between bound AFP molecules, thereby decreasing the radius of curvature from infinity to a finite magnitude. Such an increase in surface curvature leads to a depression of the freezing point due to Gibbs-Thomson effect, which states that the equilibrium melting point of a solid is related to the curvature of the particles and interfacial energy. The absence of melting at temperatures higher than the equilibrium melting temperature is defined as the superheating of solids. Antifreeze glycol proteins (AFGPs) can inhibit melting and concluded that ice in the presence of AFGPs can be superheated . Although they were not able to show quantitatively that ice was superheated, those experiments were the first to show that AFPs can indeed prevent ice from melting. They suggested that the inhibition of melting can be explained by the same mechanism as that for the inhibition of freezing with a negative curvature between bound AFPs. In this case, the ice melts between the adsorbed proteins, which reduces the volume of ice and increases the area of water-ice interface. This increases the melting point of the concave ice. It was suggested that the amount of melting suppression should be comparable to the amount of freezing suppression. However, until now there was no quantitative evidence of melting hysteresis. These classifications have been strongly criticized , who regards polymorphic transformations as non-equilibrium phenomena. Superheating or super cooling is not only possible, it is necessary. In other words, at the temperature where the two phases are in thermodynamic equilibrium, nothing can happen. According to his view, solid state transitions occur by a nucleation and growth mechanism, and the nucleation step is critically dependent on the presence of suitable defects, such as micro-cavities and other surface irregularities between crystal domains. Depending on the nature of these defects, nuclei of the new phase are formed at different temperatures and grow at different rates. three series of polymorphic transitions, of very different types, which we have studied recently. One is an example of conformational polymorphism, and the other two are examples where crystal orientation is maintained to a high degree on passing through the transitions in either direction. As we shall see, the first two seem to be best explained by nucleation of the new phases at pre-formed micro-cavities in the parent crystal, followed by their growth. The third example illustrates a special kind of order-disorder transition, where the disorder is in the stacking sequence of well defined, ordered layers. Polymorphism can be thought of as a kind of higher form of isomerism, and a polymorphic transformation as a kind of isomerisation reaction. You will not find much about such analogies in the textbooks about phase transitions in solids, for this is an area that seems to have been more or less annexed into the domain of physics. Of course, one cannot ignore the physics, and, in particular, one has to pay due respect to thermodynamic considerations, especially those summed up in Gibbs's Phase Rule: F = C - P + 2, where F, the number of degrees of freedom of the system, is related to the number of components (C) and phases (P). For Gibbs, a phase is a portion of matter that is "uniform throughout, not only in chemical composition but also in physical state". "Uniform throughout" implies that the system is regarded as continuous rather than as molecular. From today's perspective, this kind of definition leaves much to be desired, but it is remarkable how often in modem textbooks we are referred back to Gibbs for the basic concepts involved in phase transitions. The freedom of the Phase Rule from all molecular assumptions is at the same time its strength and its weakness; its strength because of its generality, its weakness because precise, unambiguous definitions of the underlying concepts such as phase and component need ultimately to be expressed at the molecular level and must also involve kinetic factors.

Please find attached herewith related articles on Hysteresis.

Thank you Prem Baboo, I had not seen that paper by Jack Dunitz before.

For a solid with free surfaces, the melting always starts from its surfaces, which are easier to melt as the atoms there vibrate more strongly than the bulk. If the surfaces are covered by some other materials that are harder to melt than the solid itself, it can then be superheated. This has been verified by experiments. 

I agree with Dr Fan Zhong's perfect answer.