The thing is, radiators get more efficient at dispersing heat as the working fluid temperature increases, and neither they nor the pumps have an increased power requirement as it does so. Not so for cooling by automanipulator - power requirement for the automanip increases as heat load increases.
Suppose a ship's normal operation will heat up the outside of its hull by 20 degrees per second. Suppose that running a manipulator to decrease the ship hull's temperature by 20 degrees per second to keep its temperature constant will increase heat buildup to 21 degrees per second.
If some other system on the ship is shut down to offset the heat generated back to 20 degrees per second, the cooling system will run constantly with no net increase due to feedback. Or put it another way, if the ship's power generation runs at sufficient overhead that activating the entropic cooler results in no change in the power system's temperature, there is no feedback loop.
Put simply, when you can make energy disappear, it's trivial to compensate for any given rate that you need it to disappear at.
Edit: In more scientific numbers, let's say that you have a figure for a given rate of heat dissipation, say 1MW of heat dissipation. That 1 MW of heat dissipation requires you to increase your energy production by 1KW, which will increase the temperature, yada yada. But if you were already generating the extra 1KW of energy, or in fact an extra 10KW of energy just to be sure, then you can maintain a constant level of 1MW of heat dissipation, and adjust your heat generation to match it by adjusting your surplus power production. Easy.