The collapse of a hydrophobic polymer in water is a basic model for many-body hydrophobic interactions that holds promise of providing fundamental insights into biomolecular folding transitions. We investigate the effect of adding progressively more attractive polymer-solvent interactions on the thermodynamics of the coil-globule transition of a homopolymer in water. We treat the thermodynamics of collapse by considering two radius of gyration dependent steps: (i) creating an equivalent cavity in water with the same solvent exposed surface area as the polymer chain, and (ii) insertion of the polymer chain into the cavity, i.e. turning on the polymer-water attractions. Changes in polymer configurational entropy and interaction energy are estimated by a mean-field theory for isolated chains. We analyze this perturbation model using extensive molecular dynamics simulations of hydrophobic polymers in explicit water.