Ok folks. First of all sorry for my poor English. I would be clearer using Spanish, French or Italian.
All of you have explained it really good and easy.
Mutt, you should read a little more about engine performances. ISA reference temperature is 15º celsius measured at Alicante (a city in Spain at sea level, crossed by the Greenwich meridian) in a special day of the year. The ideal atmosphere considers that temperature is reduced from there 2º celsius each 1000 feet elevation (Aprox).
When Rolls Royce says that an engine gives you a max of 20000 lb. is related to that point in Spain at SL, that special day of the year with 15 degrees Celsius. You can use full power every time and every place. Even at 40º or 80º Celsius. but RR does not guarantee 20000lb. Let say 15000lb. FE Hoppy has explained it easy and clear, better than me. So you are using full power but you are not using full thrust. There it is the difference. Full power but less thrust (reduced due to EGT limits)
The second point I would like to explain is that my friend Andy Rylance is mixing some concepts and I was trying to explain him the differences. He said:
If you are taking off from a 1c in temperature airport, then you need less power to take off as the air is denser.
Less power, only if you considers same atmosphere, elevation, rwy length used, TO weight etc. Less power than if the temperature with the same conditions is 20ºC and you use the same length of rwy.
From another point of view. Same airport, same conditions (TO weight, airplane etc.) and 1ºC (lets suppose ISA) In real life you may use full power (TO pwr) obtaining full thrust. If with the same conditions there is 20º C you will use also full TO pwr but you will not obtain full thrust, even you have seen the same EGT, and you will lift off at a point well beyond the one at 1ºC.
The use of derated power and how it works has been very well explained by my colleges.
Nice flights to everybody.