We investigate the microscopic mechanism of cold and heat denaturation using a 3D lattice model of a hydrated protein in which water is represented explicitly. The water model, which incorporates directional bonding and tetrahedral geometry, captures many aspects of water thermodynamics and properly describes hydrophobic hydration around apolar solutes because the hydrogen bonding rules in the model were gleaned from off-lattice atomistic simulations of water around representative protein structures. By incorporating local chain stiffness in the protein model, a homopolymer can fold into a beta-hairpin. It is shown that the homopolymer can be folded by either attractive interactions between the monomers or as a direct consequence of the entropic cost of forming interfacial hydrogen bonds in the solvent. However, cold denaturation is not observed if the collapse transition is induced by intramolecular attractions. We further find that it is the changes in hydrophobic hydration with decreasing temperature that drive cold unfolding and that the overall process is enthalpically driven, whereas heat denaturation is entropically driven.