Indeed so.ISTR that the rate of heat loss, or transfer from A to B, is proportional to the gradient between A&B.
Again, indeed, that would seem to 'obviously' be the case. However, as above, if a particular human being has less 'hysteresis' than a thermostat, it is theoretically possible that they could keep the water at a higher average temp than would the thermostat.If so surely a cylinder of hot water will lose more heat if kept at a high temperature than if it is allowed to cool?
However, it may be more complicated than that. In the case of the immersion, the water at the top of a standard DHW cylinder tends to stay relatively close to 'working temp' even when some of the hot water is used and replaced with cold water at the bottom of the tank. I need to think about whether that has any bearing on what we are talking about.
Kind Regards, John