You’re right in assuming that the Temple of Set is very much like LaVeyan Satanism,in the sense that it’s more or less atheists with a fancy hedonistic philosophy.However,I believe there’s a lot more to it.
To learn more about the Temple of Set,I think you should study Set.Setians do not worship Set,or even call on Set.Like Satanists don’t worship Satan or call on Satan.
Satanists do look up to Satan,as an ideal towards which they should strive.And to learn more on what this ideal is,just look up the 11 Satanic Statements.
The Setian ideal,aught to be Set.So study the Set of ancient Egypt.Who was Set?Why was he so special?Why did he,such a dark entity,have Ra’s favor?What about his conflict with Osiris?
Now,you obviously know how it was founded since you mention Aquino.Aquino was a member of Anton Szandor LaVey’s Church of Satan,and believed that Satan was literally appointed there by the Prince of Darkness,Satan,what he refers to as the Infernal Mandate.
Then,he claims LaVey lost his infernal mandate,and he decided to revive it,so obviously,it is slightly spiritual of an organization,but I’m not entirely sure.
It’s basis is coming into being and strengthening the ego,via the Left Hand Path,so it has a strong focus on the Individuality part of the three axioms of the LHP which are Freedom,Individuality,and Power.
There is also some connection to th aspect of Ra as the morning sun,called Khepri,but I am not entirely sure on that,right now.
The Temple of Set was one of the fascinations of mine,when I decided to go Satanist.Despite this,I put LaVey’s teachings behind me before going deep enough into Setianism.
However,I do believe that S Ben Qayin was or is a member of a small order within the Temple of Set.He said:
''As the once Head Of The Inner Order Of The Voltec, I have had years of training in shifting my perception of reality, and thus am able to successfully manipulate the ‘structure’. The Order Of The Voltec were an offshoot from The Temple Of Set, which of course is an offshoot from LaVey’s Church Of Satan - See more at: http://www.becomealivinggod.com/sbenqayin/#sthash.83R2sWGg.dpuf ‘’
So I think it’s worth asking S Ben Qaying about the Temple of Set if you’re interested.