Actually, I would do the stain treatment when the temperature is colder because the treatment has to be done with the chlorine level non existant for at least a few days and then the chlorine needs to be raised very slowly after and the pool cannot be shocked for a few weeks lest the staining return.
Colder temps mean that an algae bloom is less likely or will not be as severe and easier to treat!
(I speak from experience here and I am sure that mbar will agree with me! If you don't know who mbar is just browse the posts in this section of the forum! She has a lot of knowledge and experience with stain removal.)