The mechanism of cold- and pressure-denaturation are matter of debate. Some models propose that when denaturation occurs more hydrogen bonds between the molecules of hydration water are formed. Other models identify the cause in the density fluctuations of surface water, or the destabilization of hydrophobic contacts because of the displacement of water molecules inside the protein, as proposed for high pressures. However, it is clear that water plays a fundamental role in the process. Here, we review some models that have been proposed to give insight into this problem. Next we describe a coarse-grained model of a water monolayer that successfully reproduces the complex thermodynamics of water and compares well with experiments on proteins at low hydration level. We introduce its extension for a homopolymer in contact with the water monolayer and study it by Monte Carlo simulations. Our goal is to perform a step in the direction of understanding how the interplay of cooperativity of water and interfacial hydrogen bonds affects the protein stability and the unfolding.