Water molecules bind strongly to the polar calcite surface and form a surface-adsorbed layer that has properties akin to an apolar surface. This has important implications for understanding the thermodynamic driving forces underlying the adsorption of acid groups from crude oil, in particular, naphthenic acid, onto calcite. Free energy calculations show that naphthenic acid binds favorably to the water monolayer adsorbed on the calcite surface. However, to bond directly to calcite, a free energy barrier has to be overcome to expel the intervening layer of water. Further, naphthenic acids with longer alkyl chains bind with lower free energy to the calcite surface than those with shorter alkyl chains, and, for the same chain length, branching enhances adsorption. To better understand this behavior, for a specified alkyl chain length, we study adsorption at different temperatures. Consistent with experiments, we find that adsorption is enhanced at higher temperatures. Examination of the enthalpic and entropic contributions to adsorption shows that the adsorption of naphthenic acid is entropically favored.