Mommycarlson --
Mx6inpenn's explanation is pretty much correct. To make a beer soap I use a lye solution that is 50% NaOH, 50% distilled water. This lye solution can be a masterbatched lye solution or it can be a freshly made solution.
The boiling goes quicker than you'd think -- maybe 10 minutes to boil it down to about 1/2 the original volume. The point is to pack more beery goodness into a smaller volume of liquid.
You can add the reduced beer to the oils, stick blend a bit, and then add the lye. Or you can add the reduced beer to the lye solution, and then add that mixture to the oils. I mix the beer with the oils and then add the lye. I think this method might reduce the amount of strong odor the lye and beer can produce when they first meet.
You could use just straight beer to make the lye solution, and in that case you would not need any extra water. There's no problem with that approach, so please don't think you have to use the method I do -- you can make nice beer soap just using plain beer, as long as the carbonation has been driven off.
The benefits of making the lye solution with water and then adding a concentrated beer are these -- I can use a masterbatched lye solution, there is less chance of strong odors, and the boiling reduces the carbonation of the beer.
I don't insulate my beer soaps, but I do want them to get warm enough to gel. I put the mold on top of my chest freezer that has a slightly warm top and sometimes will cover the mold loosely with a cardboard box if the room is chilly (winter). That seems to work fine. I don't get overheating, but the soap does gel.
I hope I've answered your questions!