The short version of the CoT's history, is it's created out of the Haelynic temples desire to reunite under one Pontiff. Unfortunately none of the temples were strong enough to unite the whole of Anuire and it got more and more ugly. Culminating with the death of Rhuobher Nichaleir and Hubaere Armiendin at each other's swords.
After that the WIT & IHH squared off against each other, creating their own pontiff of the western and eastern Anuire. The OIT had at first supported the IHH against the WIT, but shifted focus after the IHH proclaimed Martin Royce as Pontiff, and turned to the WIT with an ingenious proposal... Ally against the EO and in so doing, create the Conclave of Temples with the OIT Cardinal Aurlien as it's first Pontiff.
This organisation was based on the inherent distrust between the temples. It didn't try to force one temple on all the others, but based it's influence on treaty and willing support - and most importantly: It shifted the post of Pontiff around every two years, shifting between the five major Haelynite temples.
It's creation was the basis for a legendary victory.
Conclave troops fought in one way or the other on two different fields of battle and alongside it's allies, defeated the armies of the Eyeless One and the Red Wind's gnoll army that had invaded Mieres.
Thus the CoT was an immediate success - as long as a common enemy could be found. Indeed it is very likely the only focus that the CoT will ever be really succesful at...
Presently the CoT is very likely suffering from the same problem that set in almost immediately for the victorious Pontiff Aurlien, the general level of squabbling, rivalry and fear that exists between the temples make them very wary of supplying resources to one leader. Aurlien tried to use the CoT to counter famine and epidemics on an Anuirean level, but was met with a stonewall of distrust and "we can do it ourselves" mentality. The victory was as quickly forgotten as it was won...
So to be Pontiff of the CoT is to lift a position of great responsibility, prestige and some military power (though this is de facto in the hands of the WIT, OIT & KoH) but also being the focus of a lot of distrust and worse things. Aurlien abdicated his post as Cardinal of the OIT due to some of the choices he had made as Pontiff. The two positions quite simply ended up in opposition to each other.