We use electrical power for physics experiments due to the fact that it's easy to measure. Do you follow the power of the battery/starter motor when you consider a 300HP Diesel engine?
No input power is required if your control system removes only the excess heat. Envision a system that reaches operating temperature of 600C and continues heating to 650C. A heat transfer medium leaving the reactor at 650C and returning at 600C would require input power? (hint: the answer is no) Just like we don't leave the starter motor running on a Diesel engine...
This is another area where I think you may be mistaken. Fuels, like diesel fuel, or gas, or wood, can be warmed, and might even begin to produce some "excess" heat in response. But once a threshold is passed they also go into a self-sustaining mode of combustion. Theoretically, it is the same with the sort of temperature-dependent LENR energy release you describe. There should be a low-temperature state of excess heat, but then there will be a threshold beyond which the system goes into a high-temperature state which needs radically less input energy (and in some cases maybe none at all) to sustain it. I have been calling that runaway. So far, all the data I have seen says to me that you do not have that high-temperature runaway state and instead are seeing a state of stable excess heat production. It is not in a state comparable to a Diesel engine.
This is all relevant to the system you ask me to envision. If you picture the 650C state as one of these stable, pre-runaway states that you have been displaying so far then I disagree with you. Think about the heat transfer you mention being really tiny in scale. The medium leaves at 650C and returns at 600C having given up only a tiny amount of heat energy. Do you still think that you could take away all of the input power and still have the system sustain itself at 650C? How does removing a tiny amount of heat make the system independent of outputs?
On the other hand, if you are in one of these high-temperature runaway states, then the system is already much less dependent on (or possibly free of) input energy. In that case I definitely think you could harvest some of the developed heat and the whole thing would be sustainable.