I didn't use running water because I don't own a blowdryer, but I made sure to do the treatment during the hottest part of the afternoon (which is pretty hot in May in central NC).
My journey with pasty-butt last spring: https://www.backyardchickens.com/threads/persistent-pasty-butt-in-week-old-chick.1471008/
I used a paper towel instead of washcloth and found that it sometimes helped to get the area damp, put the chick in question back into containment, and work on other...