My rationale behind Density/Temp is this:
The colder the air - the more Oxygen molecules for the same volume! The more Oxygen to burn - the less fuel required for the same thrust.
Water injection cools the air, making it more dense, AND adds more "O's" in the h2o. Nitrous Oxide does the same for Car engines.
Cruising? - Constant fuel flows at the most economic setting for the Outside Air Temperature and the range/speed required. Not too difficult really.
FMC? - ask someone else!