Inverted solubility--melting a crystal by cooling--is observed in a handful of proteins, such as carbomonoxy hemoglobin and gammaD-crystallin. In human gammaD-crystallin, the phenomenon is associated with the mutation of the 23rd residue, a proline, to a threonine, serine or valine. One proposed microscopic mechanism entails an increase in surface hydrophobicity upon mutagenesis. Recent crystal structures of a double mutant that includes the P23T mutation allow for a more careful investigation of this proposal. Here, we first measure the surface hydrophobicity of various mutant structures of gammaD-crystallin and discern no notable increase in hydrophobicity upon mutating the 23rd residue. We then investigate the solubility inversion regime with a schematic patchy particle model that includes one of three variants of temperature-dependent patch energies: two of the hydrophobic effect, and one of a more generic nature. We conclude that while solubility inversion due to the hydrophobic effect may be possible, microscopic evidence to support it in gammaD-crystallin is weak. More generally, we find that solubility inversion requires a fine balance between patch strengths and their temperature-dependent component, which may explain why inverted solubility is not commonly observed in proteins. We also find that the temperature-dependent interaction has only a negligible impact on liquid-liquid phase boundaries of gammaD-crystallin, in line with previous experimental observations