A simple model of a hydrophobic polymer in water is studied. The model polymer, a chain of Lennard-Jones particles with a fixed bond length, is designed in such a way that it undergoes a coil-to-globule conformational change near room temperature upon heating in liquid water. At low temperatures (≲270 K), the polymer chain under vacuum takes a globular conformation, whereas in water, it adopts an extended form. At higher temperatures (≳320 K), the polymer has a more compact conformation in water than under vacuum. The same polymer chain in a nonpolar solvent is always extended and shows no sign of a coil-to-globule transformation up to 360 K. The heat-induced collapse of the polymer uniquely observed in water is not attributed to the hydrophobic effect on individual monomers, but it is correlated with the temperature dependence of the potential of mean force between two monomers at contact distance.