Some interesting stuff mentioned here, but I would like to help clarify some issues regarding the Airbus autothrust system.
I will chat about the A340, but most other busses will be about the same.
First of all to understand what a "FLEX" thrust take off is we need to understand what the engine is limited to. For example the CFM56-5C4 is flat rated to 34,000lbs thrust at ISA plus 15 deg C. Meaning that this engine can produce 34,000 lbs of take off thrust up to an ambient temp of 30 deg C. Now here is the point, ambient temps above 30 deg C will force the engine to reduce take off thrust because we become EGT limited (take off EGT increases as outside temp increases), thrust being reduced to prevent us from melting the back end of the engine.
So, if our airplane is light and we have gobs of runway ahead of us, why push the engines to TOGA thrust when we can give them a bit of a break. As mentioned there are charts that the crew reference that will ultimately give them a "FLEX TEMPERATURE". This value mimics a very hot day usually greater than 40 deg C, and is entered into the flight management system which relays this info to FADEC. For lack of a better description, this fools the engines into thinking it is hotter outside than it really is resulting in a corresponding thrust reduction (provided the thrust levers are placed in the FLEX/MCT detent).
Second of all, although a smart computer, when it comes to thrust commands FADEC is a bit of a slave. Either the crew manually command it through movement of the thrust levers, or thrust signals are generated from the flight guidance portion of the FMGEC for autothrust. During a normal takeoff roll with either FLEX or TOGA selected, auto thrust is only armed, it will become active once the thrust levers are moved (manually) down to the "AUTOTHRUST ACTIVE RANGE", being from just above idle to the "CLB" detent. Movement of all thrust levers beyond the CLB detent will put you back in manual thrust which may result in a large swing in power as thrust hunts for blue doughnut position (a representation of thrust lever position on the N1 scale). In the event of an engine failure the AUTOTHRUST ACTIVE RANGE becomes enhanced to include up to the FLEX/MCT detent.
A bit of a long winded explanation, hope it is of use.
N2