Temperature-dependent properties of hydrophobic interactions are investigated by simulating the potential of mean force (PMF) between two methane-like solutes in TIP4P model water. Independent results from test particle insertion and free energy perturbation are compared to ensure that zero-PMF baselines are accurate. PMFs are computed under atmospheric pressure at five temperatures from 5 to 95 degrees C using constant-pressure simulations. The temperature dependence we observe does not agree with previous results from constant-volume simulations, highlighting the important effects of temperature-dependent water density on PMFs. Heat capacity changes upon association of two solutes are estimated at the PMF contact minimum, desolvation barrier, and the solvent (water)-separated minimum. The magnitude of the heat capacity change upon contact formation is much smaller than that predicted by the solvent accessible surface area (SASA). More surprisingly, the heat capacity change upon bringing two methanes from infinity to the desolvation barrier is large and positive. This implies that the thermodynamic signatures of the free energy barrier to desolvation have signs opposite to desolvation itself. This feature is not predicted by either SASA or a volume-based solvent exclusion model. The implications of these and other observations on implicit-solvent model potentials are discussed. Formulations based on thermodynamic perturbation and Widom's potential distribution theory are developed to relate PMF and hydration mean forces to the underlying structural properties of aqueous solutions. In particular, we provide a theoretical perspective to understand PMF in terms of local water density and the occurrences of configurations with highly unfavorable solute-solvent repulsive interactions.