The molecular dynamics with quantum transitions method is used to study the temperature dependence of the relaxation dynamics of the H2O bend fundamental in liquid water in the range from 277 to 348 K and the subsequent variation of the hydrogen bonds network in the liquid. The vibrational bending degrees of freedom of the water molecules are all described by quantum mechanics while the remaining translational and rotational motions are described classically. The participation of the H-bonds in the relaxation process is studied taking into account the dependence of the relaxation lifetimes on the number of H-bonds formed by the initially excited water molecule and the amount of energy transferred into the hindered rotational motions. It is found that the intermolecular vibrational energy transfer plays an important role in the relaxation mechanism, with almost no temperature dependence, and that the energy transfer into the rotational degrees of freedom is favored over the energy transfer into the translational motions. The thermalization of the system after relaxation is completed in a time scale shorter than the time taken for the H-bond network to recover. The relaxation and equilibration times calculated compare well with experimental and previous theoretical results.