'A work of art is not a matter of thinking beautiful thoughts or experiencing tender moments (though these are its raw materials) but of intelligence, skill, taste, proportion, knowledge, discipline and industry; especially discipline.'
Evelyn Waugh, 1960
Assume that a kiln is a hollow shape with uniform thickness of fire-brick or other insulating material. The inside is hot and held at temperature Cin , The outside is relatively cool and held at temperature Cout. Then there is a heat loss by conduction through the insulating material with is proportional to the temperature difference (Cin - Cout). The temperature at the inside face of the insulation is Cin , at the outside face Cout, halfway in between (Cin + Cout)/2, and so on for all intermediate positions in the thickness. In other words Heat loss = k x (Cin - Cout), where k is some constant number for all kilns of the same construction (shape and insulating material).
Now assume that Cin drops slowly, but so slowly that this relationship is still approximately correct. Assume further that the hot mass of the kiln is mostly inside the kiln. Then by integrating the heat loss, the temperature Cin will fall as Cmax times e (2.71828...) to the power -t/T, where T is a kiln 'time constant' dependent on the hot mass and the insulation. (See the equation in the sidebar, and a graph of this function for T = 2 hr, Cmax = 800°C and Cout = 30°C.)
T is characteristic of the loaded kiln, and for small loads of glass will not change much. Putting a heavy item inside such as a clay mold or a thicker shelf will increase T because of more hot stuff. More or thicker insulation will also increase it by reducing heat loss.
This is what is called a 'lumped model'. In a lumped model all parts are considered either mass or insulation. It is possible to analyse a 'distributed model' where the distribution of mass throughout the insulation is taken into account. For typical kiln configurations the effect on the cooling curve are not large because the rate of cooling is so slow. For fiber insulation, the effect is also smaller than for firebrick insulation.
The theory also assumes that the outside temperature of the kiln casing is fixed (heat carried away instantly), or otherwise heat is convected away approximately as the temperature difference between the kiln casing and the room air (the same pattern as the insulation). This is probably a safe assumption provided the casing is not so hot that it radiates heat as well.
What about kiln size? The total mass of an unloaded kiln is approximately specific gravity of insulation x external surface area x thickness of insulation. Thickness of insulation is probably much the same for large and small kilns, as is the specific gravity (kg/L). The specific heat (joules/°C) is also pretty much the same. So the heat content of an unloaded kiln is proportional to the surface area, and so is the rate of heat loss. Therefore large kilns can be expected to have the same time constant and the same cooling characteristics as small kilns, at least until they become really small (interior dimensions comparable to insulation thickness). Shape is simply not very relevant.
Suppose the kiln is not empty. Then it contains a shelf and work objects that add mass. It may also have differing thicknesses of insulation on the sides, roof and bottom. These all introduce minor changes in the time constant T, but a value in the range 2 to 4 hr is to be expected over the entire range of home and business kilns, except for very small ones. Really light insulation (such as fiber) will bring T smaller, but there is really no other way to increase the cooling rate except by cooling the inside too (for example using a vent or cracking the lid/door/hat open to let a small amount of hot air out and cool air in). The design of kilns is a compromise: lots of insulation makes it easy to reach high temperatures with low power, but it makes the cooling rate unacceptably slow.