I'll be using Airbus terminology here because that's what I know, but I guess the concepts are universally applicable.
The way I understand flex temperature is: It's a user interface for pilots to request a derating of engine power to reduce wear on the engine. Simple enough, makes sense.
But in understanding why this is being input as a temperature, I have often encountered confusing explanations. Many videos and forum posts will say something like this:
Flex temp will fool the FADEC to think the outside air is hotter than it actually is.
That cannot be correct, right? If the FADEC actually thought the air was less dense, then if anything it would increase engine power, not derate it.
What makes more sense to me is this:
By entering flex temp, you're intructing the FADEC to produce only as much thrust as TOGA would produce at that increased temperature.
Simple. We're not fooling the FADEC, it knows full well how much thrust it is producing and that's good.
Using a temperature value as the input (instead of some percentage of engine power) also makes sense because pilots need to be aware of this parameter anyway when considering altitude, runway length, and aircraft weigth to verify a takeoff is possible.
If I'm correct, why is this "myth" of fooling the FADEC so prevalent? I find this notion very confusing and counter-productive when learning about this. Does the FADEC even actually deal with outside air temperature in its logic? Why and how? Or does flex temp really just translate to a thrust value (possibly together with altitude)?