In theory, 9v is converted to other voltages in camera by DC-DC converters, and usually voltage doesn't matter that much because when there is more voltage, you will just draw less current. So the power consumption (watts) is still the same, and heat should be about the same....
But in reality it can be totally different.
For example sometimes it is quite the opposite. Low voltage means more current draw, and power mosfets in dc-dc converters can even overheat because of the low voltage, in some systems.
So I believe there should be some optimal voltage with least amount of heat produced.
9v could be reduced to 8,2-8,4 by adding any silicon diode in series. Diode should be powerful enough to handle at least 2A or so (current camera consumes). Cheap 1A diodes in parallel could be used, like 4-6 of them. For example 1n4004 that can be found everywhere. And diode(s) will become hot so they should be located somewhere, not in the dummy battery.