What is the camera operation technique called when changing focus while the camera is hot?

The technique described, changing focus while the camera is hot, is known as "rack focus." This method involves shifting the focus from one subject to another during a shot, creating a visual transition that guides the audience’s attention. By smoothly changing the focus, the filmmaker highlights a new element in the scene while still allowing the previous object to remain in the frame but out of focus. This technique is regularly used in visual storytelling to emphasize specific aspects of a narrative or highlight relationships between characters or objects.

Other options like "focus change" and "live focus" refer to more general concepts that do not specifically capture the nuance of a dynamic focus shift within a shot. "Pull focus," while it may seem similar, typically describes a specific type of focusing technique that does not specifically denote the broader concept of rack focus, which is characterized by the intentional movement between different focal points in a scene for dramatic effect.