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The outer skin usually has no bearing on the specific heat. Is it steam jacketed? Is it a combi with the HLT unerneath? These variables will change the temperature your MLT actuall lands at, regardless of the specific heat value.
Quick and dirty method: 1/3 to 1/2 of the shipping weight.
Some precision: surface area x weight. Surface area: 2(Pi)r(r+h) + weight of false bottom panels.
Without any extra heat variables you can use the 0.12 stainless value and input the inner wall weight to get into the ballpark. It's not important to account for any cone shape in the bottom because it doesn't significanly impact the result.
Find out the guage of the inner wall from the manufacturer. Most are 26 to 28 guage, which is 0.0156 to 0.0188 inches thick. Steam jacketed walls tend to be thinner. For these guages, the weight is right around 5 lbs per sq.ft. or 0.55 oz/sq.in.
If you have a significant amount of mash deadspace, add the weight of the water to the mashtun weight. This'll increase the strike temperature a little and can be more precise, depending on your equipment design.
Preheating definitely makes a difference. You're putting the energy into the metal rather than letting it come from the mash heat. Foundation water can do that or you can hit the side walls from the CIP spray ball(s). It doesn't matter how, as long as it's consistent and effective.
As far as the theory I was illustrating, the relevant weight is what the mash and water come in contact with. If you know the surface area and the gauge of steel, then you can calculate the weight. You can weigh the false bottom leaves or just make a WAG based on shipping weight, if known.