Globaliser:
Indeed the air conditioning system on a plane takes air from the compressor.The air is used for antiiceing systems in flight,for systems cooling,for pressurization (the cabin and all systems-for ex toilets,hydrulic sys,etc) and also for comfort in the cabin.The hot air is driven to packs (where some of it is cooled by use of heat exchangers,and air cycle machines-a compressor ,followed by a turbine which cools the air, then the cooled air is mixed with the hot air resulting the desired temperature) .
This packs are not mechanically conected with the engine.Of course they use some energy to run,usually electrical or blead air from engines.
A hotter seting of the cabin air will decrease the demand of cooled air,but with an insignificant value in flight.
The problem is like this:
If the plane is full,then we'll select a lower temp,to keep for ex 24 C in the cabin.If you have only half pax,then it's req a higher temp to keep the same 24 C .Normal.( on some planes all it's automatic,just select the desired temp)
The temp in the cockpit it's usually controlled by a diferent system then the cabin.Also,we have a lot of electronics that are also cooled,and they are also producing heat.So,my point is that a pilot will know the cabin temp only from the cabin temp indicator and also from the cabin crew.
The cabin temp sensor it's positioned somewhere in the cabin,not generally at an ideal position.On some of the planes I flew it's at a higher level,so at a higher temp,almost near the ceileing.
Also ,there are people that like 20C versus ones that like 28 C.
I usually try to keep the temp at about 24-26 C,but sometimes the temp indicator gives me a not so accurate value (for diff reasons,as I stated above)
You SHOULD tell the cabin crew to ask for or correct the temp in the cabin.Keep in mind though,that some of them may like a cooler temp (they are moving around,working),so ask another one if you feel uncomfortable.
I can assure you that we-the pilots- have no reason to keep a specific temp dictated by some fuel usage,economy bean counter,or whatever.
Brgds nice flights
Alex