Do a hard reset of the box and plug in the money. If the kinect comes on for a bit and then shuts off without the fan starting then this will probably work.
Follow ifixits teardown guide. Ignore the part where they say remove the cord first. Nearly impossible to unplug it first. Once the fan assembly is undone it will come out like any usb3 cable.
Remove the fan and look up how to make a computer chassis fan into a USB fan. Take the wires from the fan cut off the end of USB and solder them together. Then just plug that into a USB charger.
The fan will continuously but doubt it's pulling a lot of energy and you can always unplug it when you need too.
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Edit: I should note that I'm using the original fan.
Quick and easyish guide.
Disconnect the kinect from the Xbox.
Do a hard reset of the box and plug in
Follow ifixits teardown guide. Ignore the part where they say remove the cord first. Nearly impossible to unplug it first. Once the fan assembly is undone it will come out like any usb3 cable.
Remove the fan and look up how to make a computer chassis fan into a USB fan. Take the wires from the fan cut off the end of USB and solder them together. Then just plug that into a USB charger.
The fan will continuously but doubt it's pulling a lot of energy and you can always unplug it when you need too.