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Thank you for your interest in the Intel® Edison Breakout Board.
I think all your assumptions may be correct, if we take into account that servomotors have an inductive element, then a current is induced in the power line even after switching them off. And if you are using 11 servomotors, the generated current adds up, creating a considerable ripple that causes the increase in the module’s temperature.
Please keep in mind that the Edison's operating temperature is of 32 to 104°F or 0 to 40°C, so avoid this kind of behavior in order to keep the device from experiencing permanent damage.
I strongly recommend you to use separate power supplies to isolate the control part – the Edison module – and the rest of the system, in this case the servomotors. Actually, it is always recommended to use this kind of setup when running “heavy” loads like servomotors.
I hope this information answers your question.
Have a nice day.