In-situ Brillouin light scattering (BLS) experiments were carried out to measure both longitudinal and shear sound velocities of air-cooled and annealed sodium borate glasses xNa2O-(100-x)B2O3(x=10, 15, 20, 25, 30, and 35 mol%) from room temperature to temperatures behind the glass transition temperature (Tg) for each composition. This allows access to the complete set of elastic moduli at high temperatures and to study the effect of thermal history on the physical properties of the system. On heating air-cooled glasses of lower Na2O content, elastic moduli increases anomalously with increasing temperature just below their Tg, whereas this behaviour is absent in corresponding annealed glasses. This anomalous increase in elastic moduli with temperature was not observed in glasses of higher Na2O content. These differences were explained by different structural relaxation mechanisms in the glass transition range in sodium borate glasses of different compositions based on Raman spectroscopy studies in this work and in literature.