Guys, calm down. The air from outside is compressed (pressurization, remember)? This heats it, so it is cooled by the heat exchangers in the A/C packs. Cabin staff can change a thermostat, which does not turn on or off the A/C, but slightly modifies the mixing of hot compressed air with cooled compressed air.

No significance to fuel burn. Flying 5 knots slower would be a much better way to save fuel.