In response to the kinetic energy comments, it’s all governed by the simplified Bernoulli equations. When high speed air is brought to rest, the kinetic energy is converted into static pressure. The primary effect of this pressure rise is a temperature rise because of the ideal gas law. A secondary effect is the heating from the friction which may have caused the air to come to rest in the first place.
So for a static test on the ground:
Static ambient air is drawn into the engine and compressed. Both its static pressure and kinetic energy rise because of the action of the compressor blades on the air. This static pressure rise results in the major rise in temperature. Additionally the compressor is hot because of bearing friction and some of this heat will also be conducted to the air. The air friction on the surface of the compressor blades will give a rise in temperature too.
When the air is brought to rest in the cabin it expands back to its previous pressure. It will not cool back to the same ambient temperature for three reasons:
1) Entropy increase because the gas is not “ideal”.
2) The heat transferred from the compressor metal itself.
3) The heat due to air friction against the compressor blades and through the ducting.