Peri is dry when Turlough brings her into the TARDIS, just moments after being pulled from the ocean. Actually, both Peri and Turlough are wet when they first enter the TARDIS, and she is still wet when he puts her to bed. However, they are both dry by the next scene (when Peri wakes up and the Doctor enters the TARDIS) but that could have been sometimes later. It is admittedly astonishing how neat and tidy her hair is though.