The only source of heat in a gear box the energy entering from the engine.
The difference in power between input and output is consumed as friction and the only way to disperse that wasted energy is heat and noise.
If the box achieves 240F/100c it should be possible, based on the known mass of the box and assuming an ambient air temperature of 15C and no effective cooling, to work out how many BHP are needed to achieve a steady state at 100C.
Anyone a good enough mechanical engineer to do that?
Not that it really helps, as if the box is converting so much energy into heat and noise "something" is still wrong and cooling the box doesn't solve the problem, it just hids the main symptom.
