QR
More 4x required for you I think.....Latent heat is the heat associated with phase changes from solid to liquid to gas and vice versa.
If you compress a gas efficiently (say by slowly moving a piston up inside a perfectly insulated cylinder) and then decompress it again (by moving the piston back again) you will be back exactly where you started in terms of pressure, temperature and volume. The only reason why your heater works is because of the energy losses in the compressor due to air friction. And to some extent, as Extinct-Fiat says, due to contact with hot surfaces, though the casing near the front of the engine may not be much above the temp of the compressed air.