Going further in my investigation, I am trying to discover the amount of heat generated:
1DX Instruction manual page 400: With a fully-charged Battery Pack LP-E4N, movie shooting time approx. 2 hr. 10 min. at 23 degrees Celsius. Notice that this does not say anything about continuous time.
Battery Pack LP-E4N rated voltage 11.1 V DC, Battery capacity 2450 mAh --> 27,2 Wh --> 1DX power dissipation during movie shooting: about 12,6W on average.
1DC Instruction manual pages 28 and 84: "With a fully-charged Battery Pack LP-E4N, the total movie shooting time (with 4K shooting) will be as follows: approx. 1 hr. 25 min. at room temperature (23 degrees Celsius)". Notice that this does not say anything about continuous time. This also implies that 1DC power dissipation during movie shooting would be about 19,2W on average. No wonder if a better heat sink is required on the 1DC.
The 1DC camera is weather proof and has no cooling vents like some of the C cameras have. Imagine a small plastic covered magnesium alloy box with a hot 20W light bulb in it.
How long will it take before the internal temperature rises enough to shut down the camera?
Any experiences? Any rumours? Or any official wisdom?
That calculation doesn't mean that the unit will produce 12.6 WATTS of heat. That just means that the CONSUMPTION of the camera. Heat is wasted power during consumption. If the circuit is efficient, it will produce very little heat. Since most processors nowadays have some sort of internal throttling/stepping, which can allow the cores to slow down a bit and remain cool during period of lower usage, thus reducing heat generation, it is fairly hard to calculate what the actual heat generated would be. Not sure if the Digics throttle, but the cooling for processor would (should) have a sink capable of handling that heat. It probably dissipates into the chassis if it sinked (sealed, meaning no airflow). Still, if the system is efficient, the heat produced would be less than calculated.
The sensor, on the other hand, can generate much heat during operation, and since heat=noise, is sinked heavily. That is probably also sinked into the chassis. Maybe removing the rubber grips and using a heat absorbing/transmitting gel against the body to transfer heat to the dive case would get that heat away from the camera. The case should be metal if you want it to transfer to the water. If it is polycarb or another plastic, it would not transfer well. If that is the case, maybe modifying the case with a few passthrough ports and a heatsink outside (in the water) to pass some fluids/alcohol around the gel to transfer heat (like a secondary cooling loop in a nuclear reactor) would get that heat out.
You might be able to rig something using the liquid cooling system for a computer. There are copper dies that attach to processors for running the ethylene glycol through. You might be able to stick some of those to the camera body (without the rubber grips) and pass them through a dive case to some cooling fins/radiator outside. Using the passthrough ports would keep the case watertight and still let the cooling solution circulate effectively transferring the heat to the water (which should be cooler than the camera and air inside the dive case).