I have always been intrigued by the nature of the Culexus Assassains.
The other Temples most certainly possess their 'idiosyncracies'. The sterile precision and distrubingly indefatigable patience of the Vindicare; the drug-fuelled psychotic bloodlust of the Eversor; the warping and shifting physical aberrations of the Callidus; and several other non-battlefield Temples that Games Workshop has yet to produce models or rules for - such as the Venenum Temple, whose speciality is poisoning (cf. the 3rd Edition Codex Assassins, page 12)... to look upon any one of them is to gaze upon Death manifest in an incardanine form. They exist soley to inflict upon us the most exquisite of the full panoply of gruesome demises that we fallen men are sufficiently unfortunate to be afflicted with. The leering skulls, the featureless synskin daubed in a hue as fell, dark and consuming as the abyss... what unspeakable, inexplicable horrors transpire in the Pits to morph what once were humans into these relentless and compunctionless machines of destruction?
Yet the Culexus Temple is something far apart from all of the above. The Imperial Guard are human; the Space Marines are more than human; the Assassins are less than human; but the Culexi are something altogether... different. To gaze into the yawing, ravenous maw of the Animus Speculum is to plunge into the realm of insanity. A Culexus Assassin is a beast, an abomination, a hideous and appalling cosmic mistake that a flaw in the order of Creation has allowed to endure. Merely to be in proximity to one is sufficient to induce intense pain in someone.
The Culexus Temple is not merely unlike the other Assassins, they bear no relation to anything else in the Imperium. Like the blank void that is their soul, what harrowing process debases someone into a Culexus is one of the most opaque mysteries of the entire Warhammer 40,000 canon. Their aberrant nature raises many questions: what exactly are their origins, why the Imperium tolerates the existence of such patently dangerous creatures (they may be specialist anti-psyker weapons, but are such monstrous entities capable of being handled safely indefinitely?), and, like the C'Tan Phase Sword of a Callidus, where exactly their equipment originates from.
After some meditation on the matter, I would like to forward the hypothesis that the Culexus Temple is actually where the Illuminati are, shall we say, 'storing' captured Sensei.
I'm confident that people on this forum know of the Sensei-Illuminati plot, an old strand of Warhammer 40,000 lore that dates back to Rouge Trader, but here is a quick recap for those who don't.
Sensei are the ageless "sons" of the Emperor (it isn't known whether this means that they are literally the Emperor's biological sons, or men who greatly emulate him in the sense that Christ was the Son of God), and they are psychic nulls (i.e. they have absolutely no presence in the Warp) who possess the paranormal ability to manipulate and channel the energies of the Immaterium to their will - making them effectively minature walking Blackstone Fortresses. They also are afflicted with collective amnesia - they possess no knowledge of their imperial forebear, their origins, the existence of their brethren or even the full extent of their own abilites.
The Illuminati are an organisation so secretive that even the Inquisition knows next to nothing about them. Members of the Illuminati are astonishingly potent beings - they are men who have been possessed by daemons, but retain such mighty willpower, strength and faith that they have been able to defeat them alone and without assistance. The Illuminati have successfully infiltrated all branches of the Imperium, from the Administratum to the Arbites, and possess the ultimate ambition of resurrecting the Emperor - to do this, they need the Sensei, because the result of their mass sacrifice would be to rip the Emperor's soul back out of the Warp.
Now, I'm fully aware that the Sensei-Illuminati conspiracy has fallen into abeyance and is not being pursued currently by Games Workshop - but equally it hasn't been disproved either, and so I am confident that if the Development Team ever decides to recommence the storyline, their activities shall be concentrated on the Culexus Temple.
The Illuminati's hunt for the Sensei has lasted as long as the Imperium has, and as the Sensei are dispersed all across the galaxy it stands to reason that once a Sensei has been discovered the Illuminati would want to make certain that he could be arrested, controlled and managed, and not risk him eluding surveillance. Hence the notion of the Temple as a prison, where all of the 'collected' Sensei are detained. Both Culexus Assassins and Sensei are psychic nulls - and whilst you may consider this to be 'coincidental', psychic nulls are immensely rare so it's more than likely that a good few Culexi are Sensei even if the Illuminati isn't involved in them - and seeing how the Illuminati possess a presence in every Imperial department, that they could ignore these creatures is impossible. The abilities of a Culexus Assassin - particularly the discharge from his Animus Speculum - are also wholly consistent with the mastery of the Warp allowed by a Sensei.
But why would the Illuminati sponsor the creation of such monsters as Culexus Assassins? For one, you mustn't forget that the Sensei are simply tools for the Illuminati, a means to an end. They don't care about their personalities, they care about their powers. Also, it is likely that whatever insane procedure is practiced for the creation of a Culexus would wipe out whatever vestiges of independence survive in a Sensei.
And what better way to disguise a massive conspiracy than to dress it up in the trappings of official Imperial business? By having the captured Sensei battling the enemies of the Imperium, they are rendered largely above suspicion, whilst all the while the Illuminati were steadily building up their arsenal on Earth, in close proximity to the Golden Throne for ease of transport when their ambition comes to be realised...
Of course, the Age of Apostasy somewhat threw the Assassins out of kilter and now their Temples are dispersed to prevent another ravaging of the Imperial Palace by them, which plays havoc with the logistics of transporting the Sensei to the Golden Throne. This doesn't preclude Illuminati involvement, though - the civil war was of such massive scale I doubt that even they could successfully control it.
Also, we have the matter of the Ordo Sicarius, the Inquisitorial body formed to observe the Officio Assassinorum - whilst remaining virtually unheard of for ten millenia shows that the Illuminati are quite adept at destroying evidence, the Culexus Temple is such a large-scale conpiracy that some details about the true purpose of the Culexi must leak out from time to time. But just because the Ordo Sicarius exists doesn't mean that the Illuminati plot in the Culexus Temple is impossible - indeed, the Ordo Sicarius is an excellent way to tie the Illuminati and the Sensei back into an active storyline with a natural narrative flow.
Take as an example the following scenario: The Ordo Sicarius begins to become suspicious of activities in the Culexus Temple - scraps of evidence suggesting that psycho-analytical reports on the Assassins have been doctored and so forth - but as the Ordo proceeds to concentrate its energies on seeking the source of this meddling, its members are shocked to discover that a swathe of its agents in the Officio Assassinorum are suddenly 'demobilised'. Permanently.
Greatly perturbed by this unprecedented retaliation - after all, Inquisitors pride themselves on their secrecy - the Lord of the Ordo Sicarius proposes an Inquisitorial Conclave to gather reinforcements and resources and discuss who could possibly have successfully counterattacked the Inquisition in what is the very heart of the Imperium.
But as the great Conclave meets, the Illuminati, irked by the rival body's refusal to recognise a warning when it strikes them, start becoming more open and aggressive in their actions against the Sicarians, and it snowballs from there into a deadly secret war - one whose conclusion could surpass the Horus Heresy in its history-changing ramifications, but whose battling is unknown to all but the forbidding few... and perhaps one other.