Sorry, I should have been more clear with what I was quoting and replying to. Ultimately the heating comes from the conversion of gravitational potential energy, rather than any sort of adiabatic process. Fusion is also not significant in most accretion disks, though it can happen in some cases.
Your speculation of radiation pressure and/or matter outflow as a means of regulating accretion is good, and is strongly related to what is called the
Eddington Limit. A really cool small-scale example of this phenomenon may be seen with
GRS 1915+105.
It is unclear if this explains what is going on presently with NGC 253.