Isobaric evaporation, why the temperature must be constant?

[Proust]

Homework Statement

In case of an isobaric evaporation, why the temperature must be constant?

Homework Equations

I'm working on Mollier Diagram and my textbook says "because P is constant, so T is also constant", I coundn't understand it anyway

The Attempt at a Solution

 

[NascentOxygen]

I'm just guessing, but ...

if you allow a solvent to evaporate (say isobaric conditions), then by evaporating I think it will cool the remaining liquid, and this will change the conditions. So I'd say as well as maintaining pressure constant, you need to take steps to ensure the temperate of the liquid is held constant to make meaningful measurements.