I have cooled CP in the mold in the garage during winter. Do not place it on the concrete floor.
I learned long ago that those who stored their lye containers on concrete caused the lye to absorb moisture through osmosis. Whether that would happen to soap in a mold, I do not know but better safe than sorry.
That's very interesting. I had to go look up the permeability of plastic, (related to the 3rd sentence), since lye is often stored in plastic. Apparently it is a possibility, which I would never have given much thought. But I do not store my lye in the garage.
However, dry lye inside of a plastic bottle (or bucket) is not exactly the same thing as partially saponified soap batter inside of a soap mold (made of unspecified material at this point.) And then again, moisture content inside of concrete can vary based on the materials to make the concrete as well as if the concrete has a moisture problem (water pipes encased inside a concrete floor, or subterranean water leakage into the concrete, etc.) Even so, the actual mold itself would also have impact, and we all know that molds come in all sorts of materials, some of which are more permeable than others. But still... how much moisture would get sucked up through the bottom of a mold (unspecified material) in the first place. And how long would it take? And how long would someone leave that mold in the garage? When I did so, I only left it in the cold garage for a few hours or at the most overnight, not even a full day. So even if water were to be pulled by osmosis through the sanitation layer below the mold, then through the bottom of the mold, it seems unlikely there would be much actual water vapor ending up in my soap. However, in my case with these particular soaps, the molds were encased in a stainless steel cage, which is not permeable to water as far as I can find.
But either way, it's just good practice not to put a soap mold directly on any floor (concrete or otherwise), as it is considered unsanitary and not a 'Best Manufacturing Practice.' But if I had a concrete slab table (like those picnic tables at some rest areas), I'd still put down a towel or something between the mold & the table, simply because it makes for easier clean-up should any leakage occur. And, yes, I have had soap leak out of molds in the past a couple of times (not the ones encased in a stainless steel cage, though). I really would not be concerned that my soap was going to absorb water through the various layers in between the soap and the concrete. But it certainly is an interesting concept.
Inside propped up on cans, with fans 4forced air, in a chilled mold sounds like a winner!
in my finished 
In my early days of soapmaking I noticed that when I used 4-5 oz. individual cavity molds, set on the clothes dryer in the laundry room, lightly covered with a paper towel, they didn't gel.
