We investigated quadruplex formation in aqueous solutions of 2'-deoxyriboguanosine 5'-monophosphate, d(pG), which takes place in the absence of the covalent axial backbone. A series of in-solution small angle X-ray scattering experiments on d(pG) have been performed as a function of temperature in the absence of excess salt, at a concentration just above the critical one at which self-assembling occurs. A global fit approach has been used to derive composition and size distribution of the scattering particles as a function of temperature. The obtained results give thermodynamical justification for the observed phase-behavior, indicating that octamer formation is essential for quadruplex elongation. Our investigation shows that d(pG) quadruplexes are very suitable to assess the potential of G-quadruplex formation and to study the self-assembling thermodynamics.