Hi guys, this is a VERY LONG response, as I read the initial question, as well as everyone else's posts. the fridge i find is the best luck in keeping clear soap clear. freezer and room temp not always. keep in mind that adding colours and scents to your clear base, will also change its compositions... sometimes the scent you really want, just cannot be added to clear base without clouding it.
The question on whether to cool soap rapidly or slowly depends on what the soap is made out of, and what your are hoping to end up with. I do it all fairly competently, though I am certainly no visionary on the creative artistic side, like some people.
1. Cold opaque soap with vibrant colours you will often want to cool very quickly depending on what you use for colour. Some colours will start out vibrant and get dull or neutral if allowed to or wrapped and encouraged to gell. Each colour is different. Some synthetics will not change no matter what, some clays will also remain the same. You need to look at each product you use.
1. Cold opaque goat's or other milk, honey or sugary soaps you must cool quickly, as the heat of saponification will burn and scorch the sugars giving them a burnt/amonia terrible smell, and will darken your soap to brown.
-My first attempt at making goat's milk soap was an insult to all goat-kind, any creature that happens to make milk, and I believe I hurt mother nature's feelings all around.
I was at work with a partner (we are flight EMTs in northern alberta) and after finding some lye, we got to experimenting. the first batch actually turned out into something half decent, being white with half the bactch mixed with cocoa powder and swirled. Seeing this, some female colleagues asked if we could make goats milk bars as well. without reading... I guessed! I hot processed a batch of goats milk soap and it stunk up the entire ambulance bay and sleeping quarters! it turned hard brown and crusty, and we had to dispose of it behind the building! So, I read.
with cold pour milk or sugars or honey, you want to freeze the goats milk prior to mixing with lye to start, and you want to place that bowl outside in the winter as you blend your ingredients (or else a second larger bowl full of ice) and keep that lye and milk as COLD as possible! Once you mix in your oils and FO (most EO are destroyed by lye for those wishing to be all natural), stickblend to trace ASAP, pour in mold, and get outside in the snow, or else directly into your deep freezer. If you are very lucky, or you use titanium dioxide, you will wind up with a lovely white or just slightly off-white mild goat's milk soap. If you have trouble keeping things cool or get delayed pouring into the mold, or if you use just the refridgerator, you will wind up with a pale yellow to a dark orange/ light brown bar. These bars are just as mild and useable as the pure white bars, it is purely an aesthetic preference. Also, milk soaps may require being cured in the friedge veggie drawer or in a cool ventilated place as part of the leftover product of milk being pulverized by lye, is ammonia. This is usually in harmless levels and can be used, but it smells noticeably 'off'. an extra week or two ventilating, and the bars will harden, air off the undesirable aerosols, leaving you with a product you can enjoy.
3. HOT PROCESS. This is my goto choice with soap. I am simply too impatient to wait 4-6 weeks for a batch to finish curing to finally use it! I make a batch of soap, and I want to be able to test it within and hour or two! Hot process is the way you want to go if you wish to keep things 100% natural too, as all the lye is used by the time you are done, and this means you can add pure essential oils and herbs and other super fats and luxuries without any worry that they will be devoured by the lye. what ever colours you put in, is the colour you wind up with as 'gel' phase has been started and finished as you cook your batch in your slow cooker. The consistency when complete and ready to be scooped into molds is equal to that of starchy mashed potatoes, rather than the cream or pudding texture for those used to cold processing. Color options are generally more crude than with cold pours where very fine lines and swirls are possible. so, if you are making art for your bathroom as decoration, cold process is where precision and fine details can be achieved. with hot process, you CAN still do a fair bit using simple food colouring or any media you like since theres no lye. you can make layered and marbled patterns easily. What many people don't know (including a supply shop I goto where they teach classes), is that you CAN get some pretty fine lines and patterns. for example, if you use a bread pan (since the lye is gone, you can use any container you want) and you layer the botom black and the top white (or three or four layers of anything you wish) and you bend a wire clothes hanger to the same lengths or widths, you can 'barrel-roll' or up/down line, or zigag etc any pattern you choose, and when you cut the individual bars later, you will be remarkably supprised at the thin, fine lines and details. (* note, using the upper limit of water in your recipe or slightly increasing it (SLIGHTLY) will facilitate even more details. this just requires longer for the soap bars to dry harder. Mine are noticeably soft the first bar of a batch I used, but by the time i get around to the last few bars, they have hardened much more. or, make 2 batches. set one aside to harden as you use the other.
**TRANSPARENT, MELT&POUR**. detergents vs soaps.
if you buy plain transparent/translucent stock from the soap store, read the instructions or ask the store owner, as more times than not, these pre-made melt and pour stocks are not actually soaps, but in fact 'detergents'. for every day showering cleaning, the differences are slight, but that is where the similarities end. Different detergents will have different ingredients that once microwaved, scented and coloured, will react differently from each other. in general, the faster you can solidify the molecules that make up the detergents in a random state, the more clear they will be. However, each formula is made differently by each manufacturer, as such each will have different properties that is beyond what would be competent to explain here.
I make my own clear soaps, both for plain 'glycerine' soap, as well as for stock for my wife and kids to create with. like most of my soaps, the recipes vary batch to batch depending on what i have handy, what requests I have, or whatever I have read recently that influences my mind. As I am writing this long essay I doubt anyone of yous will actually read, I have just completed a large batch of clear soap, that may or may not turn out as I want *more on that at the end*. So, I poured 1 third into an empty tenderflake lard bucket and set it in my fridge, I filled up a pringles bottle for a round log, and set that on my shower windowsill, and I poured the rest into a 1 gallon plastic ice-cream bucket and set it outside in my unheated porch sitting at about -15 degrees Celcius (F and C equal at -32, water freezes at 0 degrees C. so halfway between -32F and whatever water freezes at in Fahrenheit. ) I tested my batch by spoonful in frozen cups, tweaking the batch until i was reasonably satisfied before . If you guys wish, I will tell you how things went tomorrow. The 'official' cutoff for soap to have 'clear' status, is you must be able to read size 12 text through a 1/4 inch slice. I usually aim for 3/4. These clear bars, once done, will shrink and warp as the alcohol in them evaporates over several weeks and possibly months becoming even more transparent! so even if your clear soap does not please you at first, wait! One of my worst batches ever, came out like milk. so i left it at a friend's house in his basement and forgot about them. over a year later, his wife found them. To my amazement! they had turned clear as yellow glass and were as hard as jolly ranchers candy! And I would have thrown them or reprocessed had I remembered to!
Anyways to answer the original question, the most reliable book I bought and learned from stated that cooling clear soap ASAP is the way to go. I have found however, that the batches I placed in the fridge for lack of room in my freezer, actually turned out much more transparent, contrary to what I had read... tonight, will be the first night I actually allow a log to solidify at room temp.