You should always be thinking about processes when you think about energy and entropy. Absolute energies are meaningless and absolute entropy is useless for applications outside of statistical thermodynamics (outside the scope of the MCAT). The process here is this:
protein (unfolded) ---> protein (folded)
Remember, we're talking about the shift in pKa value as the residue goes from free amino acid to protein form. We're talking about the change in free energy/entropy for this process, going from the unfolded to the folded form. The figure shows that at higher temperatures, the enthalpic contribution to free energy appears to be lower. That is, in the equation delta G = delta H - T*delta S, delta H is more negative, which would, ceteris paribus, lead to a more negative delta G. This would seem to imply that the folded state is more favored at higher temperatures than the unfolded state.
However, the point of the answer explanation is that at higher temperatures, T increases and therefore the whole T*delta S term begins to make an outsize contribution to the problem. Their explanation basically implies that going from unfolded to a folded state always involves a decrease in entropy because the protein can sample fewer states (there's a problem with this assumption - more on this later). Therefore, delta S in the equation will be negative and if T is larger, that magnifies the effect of delta S at high temperatures. So even if there is a small change in delta H, increasing temperature will result in a large, negative T*delta S term, which would increase delta G overall, making the above process less favorable at high temperatures.
The problem with this is that proteins in their folded state almost always result in a lower entropy of the system. The writers of this question err in their assumption that folded proteins will have less entropy than unfolded proteins. In fact, protein folding cannot be governed only by the entropy of the protein. Indeed, that would be paradoxical since folded proteins have less entropy than unfolded proteins by a whole lot (even more so for bigger, more complex proteins with active site structures that have to be highly conserved) and so one would expect proteins to favor the unfolded state. The key thing to remember is that unfolded proteins cause a huge entropy increase in the solvent water because the water has to form a highly ordered shell around all the hydrophobic surfaces on the protein. By burying the hydrophobic residues in the folded form, the protein releases the water from having to form that highly ordered shell and increases the overall entropy of the system. This drives protein folding.
