Usually its during the winter months that I run into a few stuck sheds until I tweak the amount of holes I need to tape up from summer time.
I use a large Tupperware type tub with holes that I melted into the lid. I then put a very small amount of water and a small wash cloth in it. The wash cloth absorbs most of the water and gives the snake something to cling onto. Mostly it helps me feel better that the snake isn't going to accidentally drown.
I put the entire tub in the home enclosure right in the middle of the temp gradient. I usually leave them there for 20-30 minutes depending on where the stuck shed is.
What happens with pillow cases is that the thread fibers expand when wet and could potentially create an air tight environment, which could cause suffocation. Generally its recommended that you use something with a very low thread count if your going to go this route.
I like using the tub with the wash cloth because it creates a nice little sauna for the snake and I can walk away from the tub without worrying about any drowning incidents.