My understanding is that since an O-H bond is being formed, the protonation step must be exothermic because energy is released upon bond formation. However, if I were to draw an energy/reaction coordinate diagram for this mechanism, the more reactive protonated alcohol would be higher up in energy than the unprotonated alcohol so I'm not sure if the initial protonation step would be exothermic or endothermic.
This problem's been plaguing me for days now.