A wet hive pillow (or quilt box) that got wet and stayed wet because the super (or quilt box) lacked ventilation.
This isn’t meant as an argument against beekeepers who use quilt boxes without ventilation. We all do what works for our bees in our local climate. Upper ventilation works for me. Someone on social media told me recently: “I close all upper entrances in winter. Hot air rises. An upper entrance is a vent to let out the warm air that the bees have used valuable energy to heat up.” While I can’t argue with that, the loss of heat isn’t as dramatic in places with relatively mild winters. Some beekeepers would argue that the standard notched upper entrance of a Langstroth hive is just big enough to release excessive moisture from the hive while being small enough to retain just enough heat for the bees to move easily between honey frames — the perfect balance of not too hot, not too cold, not too wet, not too dry.
Three days later: I placed an upside-down homemade bottom board on top to provide ventilation.
The pillow was almost completely dry within a day.