I can't emphasise enough how important it is to NOT start the APU should you find yourself with a dual engine flameout above FL250. I know that is not what is being discussed but I wonder if in the heat of battle the thought would likely come in to one's mind: after all that's what really helped Sully. (True enough)
PRO-LIM-49-20.
The reason I point this out apart from it being an Airbus limitation is that following a volcanic exercise in the sim some time back, I had a chance to try it afterward to determine if it was in fact a system inhibition logic that prevents it or a book limitation alone.
It was found, at least I the sim, that absolutely nothing will stop you from attempting to start the APU above FL250 but you will indeed cook the batteries and therefore be in a more trouble that Flash Gordon.
Airbus doesn't specify an altitude for the Sully procedure but please remember it is only for low level. That is all.