You don't actually have to drag them one at a time - if you've got a stack of multiple items, there should be a triangle in the upper left corner of the thumbnail. Clicking the triangle once will pop the stack open in a new window so you can see the individual items in it, and if you drag by the triangle, you can put the whole stack in the fridge at once.
(But, yeah, I wish there was a "put everything away" option.)