Checkerboard,
You are correct in saying that the formulae in my previous post are somewhat obscure. I employed mathematical argument quite simply because the original question was couched in mathematical terms, and required an explanation of the logic of a mathematical formula.
The point of my post was simply to illustrate that it is possible to calculate the (theoretical) FL from outside temperature, and outside temperature from FL. I deliberately left out the complexities of SAT and TAT in order to keep it simple.
The resulting formulae can perhaps better be phrased as follows:
If you know the FL and want to know the outside air temperature, divide the FL by 5, then subtract the result from 15. This will give you what the outside air temperature would be if you were flying in the ISA.
If you then look at your outside air temperature gauge (or whatever it is called in your aircraft) you will probably find that it does not agree with the figure you have just calculated. The difference is caused by a combination of the amount by which temperatures in your atmosphere differ from those in the ISA (Tdev), and (if you are flying too fast) by the kinetic heating effect due to your speed.
If you now want to know the temperature deviation (ignoring kinetic heating) simply subtract the figure you have calculated from the indication on your temperature gauge.
If however you know the outside air temperature and want to calculate the FL , subtract 15, then multiply by 5. Ignore any + or - and you have the FL. Once again any error will be due to a combination of Tdev and kinetic heating.
The original post suggested using the first 2 digits of the FL. This is OK if your FL is three digits but is no good if it is only 2.
For example if we use the first 2 digits of the FL we will get the same result at FL10 as we will at FL100.