Thermoresponsive polymers exhibit coil-globule transition in aqueous solution where the polymer undergoes transition from the coil-like morphology to a globular form with the change of temperature. Such transitions also reflect changes in the solvent dynamics captured by various spectroscopic methods. In this work, we construct a phenomenological model to capture the dynamics of the NMR relaxation of water molecules of an aqueous solution of thermoresponsive polymers that are known to form hydrogen bonds with the solvent water molecules. The model relies on the behavior of the polymer-solvent hydrogen bonds and the sharing of rotational kinetic energy of water molecules in the vicinity of the polymer chain and the bulk. This is shown to provide a direct estimate of the fractional change of the polymer-water hydrogen bonds across lower critical solution temperature from NMR relaxation data of solvent water along with a reliable estimate of the transition temperature. In addition, it also provides a measure of the dispersion of the strengths of these hydrogen bonds. We exemplify the validity of this model by successfully fitting the experimental data to show that the extracted parameters provide significant insights into the role played by the hydrogen bonds in the process. The possible extension of this model to solvents that form no hydrogen bonds with the polymers is also discussed.