Personally when we tore out our horrible kitchen cabinets years ago, I hung several of them in my basement and installed those plastic coated wire shelves inside. That is where I cure and hold my soaps.
I didn't have any problems with it getting hot, but I was going back and forth, blend for about 30 seconds, then whip or stir with the blender.
As for curing, try setting up a fan right by them. So long as it's not sticky humid out it should work.
Neko dive right in!!! Trust me, it's not anywhere near as scary as some people make it sound. I put it off for years because of all the hype online about the lye. After my first batch, it's nothing as scary as some people make it out to be. YES, use caution, but basically treat it like a big pan of boiling water or a pan of hot bacon grease. I don't personally use any safety equipment. I just mix my lye and water in a wide-mouth wine bottle, cap it with a pop top and swirl it around. That prevents the vapors from getting to me. Before I found this bottle, I accidentally breathed some fumes. It's not exactly like a spa treatment, but it wasn't really that terrible.
I realize this is an old post, but to make soap dry faster you can do what is called water discounting. Using your lye calculator, drop the percentage of water down to no less than 25% (I think most lye calculators use around 35-37%). Any less than that and it may not be enough water to get the lye fully disolved. You have to be sure your lye solution is cooled adequately and work fast.
I store my in pop/beer flats (card board) lined with wax paper for a few days, then put them in a cabinet. They do fine, I hope to get one of the bread racks the store uses or something simular to use in the future.
Those plastic mesh sheets or plastic canvas they use for yarn crafts work well for lining a box or a shelf to dry soaps. It keeps them up off of the bottom of the box enough to help them dry faster.