The temperature dependence of the vibrational sum-frequency generation (vSFG) spectra of the air/water interface is investigated using many body molecular dynamics (MB-MD) simulations performed with the MB-pol potential energy function. The vSFG spectra calculated for different polarization combinations are then analyzed in terms of molecular autocorrelation and cross correlation contributions. To provide molecular-level insights into interfacial hydrogen-bonding topologies, which give rise to specific spectroscopic features, the vSFG spectra are further investigated by separating contributions associated with water molecules donating zero, one, or two hydrogen bonds to neighboring water molecules. This analysis suggests that the low frequency shoulder of the free OH peak which appears at similar to 3600 cm(-1) is primarily due to intermolecular couplings between both singly and doubly hydrogen-bonded molecules.