The structure and dynamics of the hydrogen-bond network in water is investigated as a function of the temperature through the application of a first-principles approach that combines an ab-initio-based water potential with an explicit quantum treatment of the molecular motion. A molecular-level picture of the rearrangement of the hydrogen-bond network is derived from the direct analysis of linear and nonlinear vibrational spectra. The results indicate that good agreement with the available experimental data is obtained when the temperature scale is defined relative to the corresponding melting points. In particular, the theoretically predicted energy barriers and time scales associated with the hydrogen-bond dynamics are closely comparable to the experimental values obtained from two-dimensional and pump probe infrared spectra. The present analysis will also serve as a guide for future developments of an improved ab-initio-based model capable to reproduce the properties of water in different environments and under different conditions.