I don't know remotely all of the chemistry and physics of soap, but what I have learned is that a bar of soap is not a big solid piece of ... well ... soap. Soap is made of sheets of big, long soap molecules separated by layers of tiny water molecules and water-soluble salts. It is not really a solid -- it's a complex mixture of solid and liquid phase components.
The soap structure, as I understand it, reminds me of the clay found in soil. Clay has a similar layered structure and chemically active properties. These qualities give clay the unique ability to adsorb then slowly release water and nutrients. Plants thrive much better in soil with some clay in it for this reason. But I digress...
As clay dries out, the water gradually migrates from between the sheets of clay molecules. What is left between the clay sheets is an increasingly concentrated soup of water-soluble molecules and ions dissolved in the water that remains. As the clay gets drier and drier, the clay layers compress tightly, trapping the water solution in its structure. Very dry clay is difficult to rehydrate. The sheets have to open up again to allow water into the structure so re-hydration can occur. That can take a LOT of soaking.
If soap behaves even a little bit like clay, it will release water fairly slowly during its cure due to its layered structure. Low humidity and moderate warmth will certainly be helpful and necessary, but the curing process is not remotely the same as just evaporating the water off a wet sidewalk. It can be helped along a little bit, but can't be hurried a lot.
When the soap cures long enough, excess water will have migrated out of the soap structure and the sheets of soap molecules will be tightly packed against each other. This will make the soap physically harder, and the tightly packed layers will also reduce the water solubility of the soap.
I suspect there are other more subtle chemical changes in the soap molecules during this curing process that contribute to the change in feel and lather, but that's a topic I don't have much of a clue about.
--DeeAnna
PS: A very rough analogy -- take a half dozen sheets of plastic food wrap. Lay one sheet flat on the counter and spray the top surface with water. Lay a second sheet smoothly on top. Spray it with water. Lay a third sheet on top ... and so on. Now try to evaporate the water from between the layers of plastic. A fan will help ... a little. Low humidity will help ... slowly. Too much heat will just cause the plastic to melt or distort. That's not going to be a fast process no matter what you do. The best solution -- low humidity, moderate warmth, and patience.