Nice thought, but unlikely outcome. The little cat can wouldn't hold enough water unless it is one of those huge, multiple feeding ones.
The freezer bags would work, but again I would put it in the corner with bedding between it and her (upright), but not under the bedding/on the base of the nest. It should be close enough she can inch towards it if she is hot, but also be placed so she doesn't have to be on/next to it...so the farthest corner from where her 'nest' is within the nest box. You don't want her to become chilled, nor move to another nest box because it is too cold.

Why not fill the little cat dish with frozen corn kernels? A two-for-one special. Cooling and food! Every couple of hours in the middle of the day, top it up when you take her off the nest.