It seems that placing a (black) hat in a freezer will actually stiffen or harden it, at least temporarily. Is there an issue with doing this on Shabbos, if there is no change in the shape of the hat? Thank you.
I am not aware of any problem with this. If you have a specific reason to assume it is a problem, please let me know.
It isn’t bishul, because bishul only applies to making items hard or soft with a fire. See Rambam Hilchos Shabbos 9-6, Chochmas Adom Shulchan Aruch Horav 318-6.
It also isn’t molid because the item is not changing form.
It isn’t tikun moneh because it isn’t broken that it should be called fixing. Besides it will go back to its original state very quickly. MG:A O:Ch 308-34.