Until recently no definite experimental evidence of a presence of strain and/or of reconstruction of the surface structure of nanocrystals has been presented. Using powder diffraction techniques we were able to determine the atomic structure of nanocrystalline grains. In a series of powder diffraction experiments, using synchrotron and neutron sources, we showed that powder diffraction techniques can be effectively applied for studies on nanopowders with crystallite dimensions below 20 nm and can differenciate between the structure of the grain interior and its surface. A meaningful and unique interpretation of such diffraction experiments requires that the data are collected in a large diffraction vector range, 150 nm-1 or more. We evaluated the structure of nanocrystals of SiC, diamond, and GaN using the following characteristics: (a), the type of strains at the surface (compressive or tensile), (b), the profile of the strain field, (c), thickness of the surface layer and, (d), a response of the lattice of the grain interior to the stress exerted by the surface atoms. In this paper we report preliminary results of examination of thermal properties of SiC nanocrystals aiming at, (1), determination of the thermal expansion coefficient and, (2) the Debye temperature, assuming that thermal vibrations are different in the grain core than at its surface. The experiments were performed at SNBL station, ESRF, Grenoble (wavelength of 0.05 nm) in the temperature range of 130 - 920 K. We examined 15 nm SiC powders: (i), as synthesized, (ii), sintered under high-pressure high-temperature conditions, and (iii), embedded in a nanocomposite with (Zn + Al) matrix. The elaboration of the experimental data is based on the theoretical diffraction patterns calculated for nanocrystals with different thermal vibrations modes.