The authors investigate equilibrium properties of a simple model of hydrophobic polymer in aqueous solution by means of dynamic Monte Carlo simulations. The solvent is described by a simplified two-dimensional model, defined on a triangular lattice, which has been previously shown to account for most thermodynamic anomalies of pure water and of hydrophobic solvation for monomeric solutes. The polymer is modeled as a self-avoiding walk on the same lattice. In this framework, the degrees of freedom of water are taken into account explicitly, and in principle there is no need to introduce effective self-contact interactions for the polymer in order to mimic the hydrophobic effect. In certain conditions, the authors observe low-temperature-induced swelling, i.e., expansion of the polymer globule upon decreasing temperature. The authors discuss the relationship between this phenomenon and the anomalous properties of the solvent.