isobaric evaporation, why the temperature must be constant?

Proust

1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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.