From the game's encyclopedia
A Temporal Head of Faith acts much like a normal Ruler, with the Head of Faith Title being destroyed should they lose all their land.
Should the Doctrines of the Faith allow for Great Holy Wars they will be Directed (e.g. Jihads).
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Temporal Head of Faith is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Temporal Head of Faith acts much like a normal Ruler, with the Head of Faith Title being destroyed should they lose all their land." It is part of Head of Faith. The game also links it as Temporal. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.