The entropy penalty of solvation for nonpolar solutes dominates the hydrophobic effect at room temperature. We find that this entropy arises from a competition between a relatively localized "two-body" term, and a contribution arising from non-pairwise-decomposable three-body and higher-order terms. We use a full, angular dependent, expansion of solute-water correlation functions over the full range of fluid temperatures for a two-dimensional model of water. This water model has been shown to capture many of the basic anomalies of water and aqueous solutions of sparingly soluble nonpolar molecules, including the volume anomalies of water and the thermal anomalies of the hydrophobic effect. Our results show that for hot liquid water, the two-body approximation is sufficient to estimate the transfer entropy, but in cold liquid water, which is the main regime for biological hydrophobic interactions, the two-body assumption substantially overestimates the degree of ordering in water.