Heating the Crucible
In QFS parlance, this expression means receiving shocks and using these as catalyst for internal change, generally for building cohesion between little I's.
In order to do, one must be. But one cannot be, nor wish, nor do, without having internal consistency. Without internal consistency, action just happens as a result of activating one or another program which happens to have been installed by circumstance into the person.
Heating the crucible involves internal friction, a struggle between yes and no, as Gurdjieff puts it. Little I's and programs cannot be discovered unless they are activated and one attempts to work against their pull. Heating the crucible, i.e. receiving shocks and working against one's default responses while remembering oneself is a way of first knowing oneself and then creating cohesion.
The word annealing, which means repeatedly heating and cooling a piece of metal while shaping it, relates to this process. Several repetitions of the same or similar shocks are needed for achieving permanent results.
Cooling too fast makes brittle metal and in the allegory would correspond to self-calming, i.e. denying or rejecting the shock or dissociating it. Not cooling at all is not good either since one cannot function in a state of permanent shock, besides this too leads to dissensitization which is not the objective.
The word crucible is used in alchemical language probably to denote the human as a whole. It is a vessel in which a substance is being prepared. Gurdjieff uses the analogy of a chemical factory for the same or similar concept. The terms just come from different ages and cultures.