Different species of snakes lay in different conditions.
Some like to lay in rotting material at the surface (IE leaf piles, logs, etc.) but my understanding is that kingsnakes, at least L getula if not all getula, in the wild lay where the sun don't shine - where it is completely dark, humid, and proper temp.
As far as vermiculite etc. - in a proper incubator the temperature is probably just as stable if not more stable than where they lay in the wild.
In a house where the room temperature doesn't rise above 82F it is probably good enough.
If like the OP or me, internal room temperature hits 90F on the hot days - then unless you take measures to provide cooling to eggs, they will be warmer than where the wild kings lay their clutches.
Typical 6 qt sterilite tub will have about 200g - 250g of water in it. That's not a lot. Most of the thermal capacitance of your incubating media will be from the water. Out in nature, there's a lot more water so it takes a lot more energy to raise the temperature of an underground nesting box. The ground above acts as insulation to the chamber where the eggs are laid - just like basements tend to be cool on very hot days. btw - the local indian tribes, when they built their shelters - they dug into the ground for the same reason, it provided cooler temps.
Go out in your garden on a hot day - and dig down just 12 inches - it will be cooler than the surface.
On the really hot 110F days it certainly is cooler in my house than outside - but at >90F insude it still warm enough to kill eggs of the same species of snake that breed on the hill behind my house if I don't take additional measures.
Soil, largely due to water content, makes for far excellent insulation - and kings lay underground.
Take a typical tub of incubation medium stabilize it to 80F. Then put it in a room that is 90F - it doesn't take long for it to heat up to the egg killing danger temps. There just isn't enough water to resist the thermal change.
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3.6 L. getula californiae - 16 eggs (Cal. King)
1.1 L. getula nigrita (MBK)
1.0 Pantherophis guttatus guttatus (Corn)
0.1 Pituophis catenifer catenifer (Pacific gopher)
3.3 Elgaria multicarinata multicarinata (Cal. Alligator Lizard)