Ok I am getting some of this....
one of the limiting factors is the Exhaust Gas Temperature, so putting very hot air into an engine you cannot add as much heat to the air compared to if it was cold - ok got that seems to make sense.
Now this "fooling the engine into thinking..." part... well why does an engine have to be fooled? Surely modern Flight Management Computers you can say "I am at this weight today, which is lighter than usual, the outside temperature is this, so work out how much power/thrust I need to get off the ground..." Why do you have to start putting in false figures to fudge the result so you get what you want?