Frank, a 250W rating normally relates to the safe continuous power output of the motor.
If it has an efficiency of 80%, it would need to consume around 313 Watts of power in order to produce an output of 250 Watts.
So your 360 Watts of consumed power is actually producing around 288 Watts of output. (Only 15% more than it's rated output)
As long as the motor does not get too hot, you should not have a problem.
It's the excessive build up of heat that tends to cause motor failure by melting the insulation on the wires, resulting in a short circuit.
From what I've seen, the insulation on the hall sensor wires seems to fail at a lower temperature than the lacquer on the windings themselves, causing failure of the hall sensors.
Running a 24V motor on 36V
At full throttle, I would expect a 24V motor to run 50% faster than a 36V motor using the same 36V supply.
The 36V motor should draw less current and therefore generate less heat because it is actually doing less work!
So under maximum load, the 24V motor would probably fail before the 36V motor as it will be drawing 50% more current and working 50% harder, but if both motors are run at 36V, and limited to the same 10A current, I don't suppose there would be much difference between them.
Alan