What does "a good heat exchanger" look like in this case? You compress air, the pump heats up, so you ventilate it to keep it cool. The air in the tank is hot, and starts to cool as it sits in the tank, and this causes a decrease in pressure, which is why even with no leaks a shop air compressor will run for awhile, stop, then after awhile cut back on again.
I get that I'm applying a shop tech's "machines that I can move with a hand truck" understanding to factory-size operations here but...