Sorry but I disagree with all of you! As hovering says, if the air is compressed and then expanded why does it not end up at the same temperature? It would not matter whether it was mixed with cold air -the cold air is at roughly atmospheric pressure so the hot air must have expanded before its mixed, at which point it will instantly cool - it won't take any time to cool, same as it doesn't take any time to heat up when its compressed (just as well otherwise your diesel car wouldn't run!). There is no delay because there is no movement of energy as would occur with a constant-pressure heating from, say, an electric fire. (I think the word I am looking for is "Adiabatic")
HP - in the 332L the air decompresses at the heater valve which is away from the engine casing.
In fact hovering has it correct when he says "friction". It is the extra work done to the air by the compressor that raises the air's temperature by a greater amount than would result from the compression. So when the air expands again its hotter than when it started.
Think of it in terms of conservation of energy. Unless the compressor is 100% efficient (which nothing is!) the extra energy required to drive the compressor above that used to compress the air has to go somewhere - and of course it goes to heating up the air by friction.
Another example for 332L2 / 225 pilots with the hydroelectric generator is the hydraulic heater. This maintains the temperature of the LH hydraulic system within a certain range simply by bleeding high pressure fluid through a restriction back to the reservoir. The fluid is incompressible and the heating effect comes purely from friction through the restriction, plus perhaps because the pump is having to work harder.
And another one - why does the main gearbox oil heat up? there is hopefully no metal-to-metal contact, no combustion etc. The heat is purely the result of thrashing the oil around and squeezing it through bearings etc - ie friction in a fluid
HC