Richard J Kinch wrote:
Don Foreman writes:

Real compressors aren't isothermal so the
compressed air is hot. Some of the work done by the compressor goes
into heating the air, and that heat is lost to the environment so the
process is inefficient.

Compressed air is hot (has a high temperature), not so much from the
addition of heat, as from the compression.

Yes, that's the way a heat pump works.