"Heat" is really entropy gain, and so in order to do useful work you have to increase the entropy of the system to higher and higher quantities. If you want to move entropy from one closed system to another(to cool one system down) then you must emplace even more entropy in the one system than you removed from the other because you must spend entropy(generate heat) in order to force a change in the state of the other system. It's a fundamental law of physics. You cannot reduce the entropy of the universe by any means.

This is true whether you use an engine, a river, or a solid-state fully electronic device. Even humans must obey this law, and indeed there has to be some air movement for us to cool down using our sweat, and interrupting or changing that air movement costs energy and therefore increases entropy somewhere.