When you create a new character, you can choose to start him as a hero. Heroes can't inherit from dead characters, and they can't be inherited from.
When creating a hero, you choose his life goal. Slay a dragon, smith a q9001 sword, bang all the fair maidens in the kingdom, stuff like that. Upon achieving his goal, the hero immediately ascends into godhood, leaving some sacred relics where he stood. If he dies without achieving the goal, all the effort that went into him is lost. The new god's portfolio and power depend on the nature of the goal he had to achieve to ascend.
Relics can be placed in shrines. They can be stolen, but they can't be destroyed. Anyone can make sacrifices to a god at his shrine. It works like ancestor worship, except gods will tend to ask for items related to their portfolio. In return for sacrifices you can get divine inspiration (maybe even have it random as opposed to numen expenditure) which lets you craft a single item of increased quality, unlocks a new recipe or something like that.
Too Greek?