Most of the items on the mythic boon list would work rather well for hero points, substituting "a creature whose hit dice or level is higher than the PC's level" for "mythic creature".
The last group I played in gave out one per session. If you didn't use it, you lost it in between sessions. Once when we leveled up. And one for doing something particularly heroic, outside of the expected "I hit it with a stick and saved the princess".
In our campaigns, they reset to 3 with each level (no carry over). So, you are encouraged to use them as a player. Though most players will generally use 1 to sway a big save and "save" the other 2 to prevent a death.
Though I like the idea of awarding bonus ones when a character does something particularly heroic.
Never hand out hero points. Instead, let your players 'be heroic'. Your characters should be able to both 'survive' and 'do great things' without having to spend a 'fiat point' to do so.
Encourage out-of-session content, like interesting descriptions of downtime activities, journal entries for the PCs, additional backstory, drawing maps or drawing PCs or something similar.
It gives the players something to do between sessions, and helps to chronicle the campaign so you can look back on it in the future and be like, "Oh yeah, I remember that, that was AWESOME!"