Wow, it's first time that it has happened to me! The salt soap is sweating! I have made salts soaps in summer and winter, humid and dry weather but never had sweat on salt soap. I believe that the only explanation is the recipe since this one is totally different from what I have done before.
In my salt soap recipes there is usually a very large percentage of coconut oil and then some butter. The lowest that I have gone is in the Summer Spa where I used 50% coconut.
This recipe has 30% coconut oil and 70% rapeseed oil with 5% superfat. It is a test batch I made with my sister Suvi to experiment how different percentages of sea salt affect the soap qualities (I'll let you know about the results once we have thorougly tested the soaps). Patience is not one of my virtues, so we used oven hot process to be able to test the soap sooner. After the soap came out from oven, we divided it in four parts and added different amounts of sea salt in each. The one with no sea salt did not sweat but even the smallest amount of salt resulted in sweating!
All this makes me conclude that the recipe or certain oils in the recipe might cause sweating. What do you think?