Thanks for the responses
DaveReid, you say "Would that not imply that the pressure inside the cabin would be then equal to ambient? But it obviously isn't."
I think your point is that since the air is ** flowing** into the cabin, there must be some pressure differential. However, I think the pres differential is almost zero, for example I would still get some air with the cabin door open, and there is no pressure bump on ears or showing on the cabin rate of climb.
Flypaddy and Goldenrivett, thanks for your explanation. Goldenrivett you say
"The air has been given a huge amount of Kinetic Energy by the compressors as well as the static pressure rise. The KE is responsible for the temperature rise."
There is also a decrease in kinetic energy almost back to zero, as the air entering the cockpit is very slow, and I'm on the ground with the engines running. Does the air also cool as the kinetic energy decreases?