Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical ensemble. There are constraints on these distances, which are shown to explain some characteristic features of the caloric curve in very small clusters containing 3 or 4 atoms. We anticipate that this approach could give a novel insight into the phase transitions in larger clusters as well. During these studies, we have established a very general and rather simple result for the Jacobian determinant of the change of variables from Cartesian coordinates to mutual distances, which is of wide applicability in the N-body problem.