Number of the experimental NMR distance restraints extracted at the ambient temperature is remarkably decreased by an internal mobility in a molecule, mostly chemical exchange. This problem can be avoided by NMR measurements at lower temperatures. To achieve the lowest temperature while keeping the liquid state and minimize the chemical exchange, the NMR experiments can be performed using the slowly cooled capillaries. The aim of the present study is to investigate possibilities of NMR measurements in liquid state at the temperatures below 273 K and applicability of this approach to a nucleic acid fragment. For this purpose, the d(GCGAAGC) hairpin has been chosen because its structure has been previously solved precisely by NMR spectroscopy. We have performed a new structure calculation of this molecule using the low temperature NMR measurements and compared the precision of the newly calculated and known structures. A series of the 2D-NOESY spectra with the mixing times in a range of 50 to 400 ms has been measured at 268K. The NOESY cross-peaks for the different mixing times were integrated using the SPARKY program and the results were employed to derive the inter-proton distance restraints. Then, the numbers of distance restraints extracted at 268 K and 303 K were compared. In case of nonexchangeable protons, these numbers were comparable due to the significant spectral overlaps in the NOESY spectra measured at 268 K. While, there was almost twice higher number of exchangeable proton distances extracted at 268 K compared to 303 K and these restraints helped increase the precision of the calculated structure of the d(GCGAAGC).