Thermodynamics (well, equilibrium thermodynamics) doesn't say too much, because evaporation is a non-equilibrium effect. They're not saying more water vapor is

Thermodynamics (well, equilibrium thermodynamics) doesn't say too much, because evaporation is a non-equilibrium effect. They're not saying more water vapor is produced for free given the energy, rather that the _rate_ of evaporation is increased — and that is up for grabs.