I vaguely remember this game having some kind of heir/succession thing in place, where if your main character died, they'd get replaced by some sort of nominal 'heir' character that was provided by your temple.

Is this the case or am I really misremembering stuff?

I believe there is a succession thing. To get heirs, you have to conquer other factions by capturing their great temple before they do. Or at least that's what I recall--just purchased the game. Downloading the game now to confirm!

The only way to get heirs is by liberating the Great Temples of factions that are at least neutral towards you. Factions that have already liberted their temple or that have a bad opinion towards you will consider this an act of war. The better the relationship you have witha faction, the more units and resources they will give you for liberating their temple.

As greyhuntr said, liberating temples of friendly factions before their faction leader is killed, is the way to do it. However it isn't actually all that hard to make a faction friendly to you. All you need to do is talk to them, and gift them all your spells. Perhaps a couple of artefacts too. Using that method I managed to get heirs of 7 other factions when playing as Balkoth (easy to get good mages and therefore lots of spells).

All seven other factions? I though Life started out with their temple liberated when you play as Death

Sorry yes, I meant six.