Why warm water and slow circles are the point of washing your face
Most people already run the tap warm and rub in small circles without thinking about it. There is a plain reason both habits work, and it has to do with oil and time.
Why the water runs warm
Almost everyone turns the tap to warm before washing their face, even in a flat where the hot water takes a minute to arrive. The reason is fat. Sunscreen, sebum and most makeup are oils and waxes, and fats loosen as they warm. A cleanser contains surfactants, molecules with one end that grips oil and one end that grips water. Warmth helps those molecules get hold of the oil so the rinse can carry it away. Lukewarm is the usual target. Very hot water takes away more than it needs to, and that is a good reason to stop short of steaming.
Why the circles are slow
The second habit is the small circles. Surfactants gather oil into tiny clusters called micelles, and that takes a little time on the skin. A quick splash does not give them much. Light, slow motion spreads the cleanser evenly and nudges loose whatever is sitting on the surface. Pressing harder adds nothing to the chemistry, and it is where irritation tends to start. That is why a minute of gentle massage feels right without anyone being told how long to do it.
This is also the idea behind a silicone cleansing brush. The silicone is nonporous, so it does not soak up water and cleanser the way a washcloth can. A small vibration sets the pace, and a warm tip supplies the warmth for you. Whether it does the job better than clean hands is a matter of taste, not measurement. Hands do the same work, and plenty of people prefer them.
What to keep from it
The whole habit comes down to four things: warm water, a full minute, a light touch and a thorough rinse. Dry by pressing a clean linen or cotton towel against the skin instead of dragging it. If a brush is part of the routine, let it dry out in the open between uses, on a shelf with some air around it. A damp tool in a closed drawer is the one real flaw in the idea. Everything else is the same plain habit you already had, with a reason attached.