The Aircon system in flight is actually heating the cabin, to counteract the temp outside of the aircraft which could be down to -60 deg C. So by setting the temp lower would infact reduce the load on the A/C. However as the environmental control system maintains a certain amount of flow, this flow would not change and there would be no change in bleed air use. So the end result is no change in fuel use.
Mendareo you are sort of right. The Airconditioning system is, in the 'big picture', warming the cabin in cruise. But the aircon pack actually ALWAYS COOLS bleed air from about 180C down to whatever the 'demand' is. I'm not going to get too involved with, what the demand is, considering this is just a Pilot's forum
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You are certainly correct as to this comment.
the environmental control system maintains a certain amount of flow, this flow would not change (at least in response to a temperature change demand) and there would be no change in bleed air use.
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I could also add that the crew makes the demand for temperature, and temperature demand in an Air Cycle Airconditioning system has little relevance on fuel consumption on the engines from which that temperature is derived.
K