strantor
Not to belabor the issue, but, how do you plan to keep the pressure differential zero? Hydraulic fluids change volume with temperature and, once filled into the motor, you either have a vacuum when it cools (from not running, if filled with hot oil) or pressure when it heats up - even 10C is a big deal when the device is completely filled with oil (no head space). Paraffins/mineral oil have linear expansion of 100 ppm/degree C whereas steel is about 10 ppm /degree C). On a volume basis, that is a cube factor (30x more in volume change). You can estimate the heating of the oil by measuring the difference in current draw when the motor is run empty vs. full of oil. That is the energy pumped into the oil. The heat loss to the water is more difficult to calculate but wall thickness of the pump housing, an estimate of pump surface area and the heat transfer co-efficient of steel should give a rough estimate if the pump will gain additional heat or lose heat to the surroundings when it is 10 degrees C warmer than the water (compressibility of your hydraulic fluid will be needed to determine the pressure increase).
In other words, if the pump is filled cold, runs and warms up at any pace while underwater, you have no fear of getting mineral oil in the pump until it shuts down and cools. That is because the seals on the pump will likely leak the first time it warms up and will suck in water through those blown seals when it cools down.