The population of small bodies of the outer Solar System is composed by objects of different kind and size, such as comets, Kuiper Belt objects and Centaurs, all sharing however a common characteristic, that is to be rich in ices and other volatiles. The knowledge of the composition and properties of these bodies would help in better understanding the processes that shaped the solar nebula at large heliocentric distances and determined the formation and evolution of the planets. A large number of observational results are now available on these bodies, due to successful space missions and increasingly powerful telescopes, but all our instruments are unable to probe the interiors. However, we are beginning to see how these seemingly different populations are related to each other by dynamical and genetic relationships. In this paper we try to see what could be their thermal evolution and how and when it brings to their internal differentiation. In fact, in this way we can try to foresee what should be the surface expression of their differentiation and evolution and try to link the surface properties, as probed by instruments, with the interior properties. One thing to note about the cometary activity is that it is well interpreted when assuming that the comets are small, fragile, volatile-rich and low-density objects. This view, despite of the strong differences noted in the few comet nuclei observed in situ, has not been disproved. On the other side, the observations of the Kuiper belt objects are possibly indicating that they are large, probably collisionally evolved objects (Farinella & Davis 1996), maybe with larger densities. We are now facing a kind of paradox: we have from one side the comets, and from the other side a population of much denser and larger objects; we know that a dynamical link exists between them, but how can we go from one type of population to another? In this paper the current status of our knowledge on the subject is reviewed, taking into account the results of thermal modeling and the results of observations.