I don't think you need to increase the heat flow to capture the free energy? If I find a hot bath that is just haphazardly dumping heat into a cold bath, increa

I don't think you need to increase the heat flow to capture the free energy? If I find a hot bath that is just haphazardly dumping heat into a cold bath, increasing entropy unnecessarily, it's perfectly possible for me to stick a heat engine in between them and capture the free energy from that flow (averting entropy creation) without actually changing the heat flow (joules per second) between the baths.