When the old ladies talked about the jobs they had to do as girls before the Great War, I doubt if they thought of bed warmers as waste heat recovery devices rather they were just part of another chore.
I recently came across one in a house clearance shop whilst looking for draw handles. The concept is simple, just before bedtime, the copper pan is partly filled with hot ashes from the grate and the lid pushed down securely. The hot pan is then pushed into the foot of the bed and moved around until the sheets were warm. The procedure was not without its risks, not least of which was danger of scorching the sheets if the ash was too hot and there was also the possibility that the lid would come loose and dump ash into an otherwise clean bed. In establishments inhabited by lewd males, the operator needed to ensure that she was safe from unwelcome attention whilst bending over.
Before the days of laundries and tumble dryers it was difficult to get bedding dry after washing during winter months. Damp bedding was not only unpleasant but also perceived as a health risk. Respiratory diseases are less common than they used to be, but at the turn of the century they were greatly feared. When I was very young, my mother used to put library books in the oven to kill germs, behavior which now seem bizarre and at school in the early 1960s were were all screened for TB. Dry bedding was thought of as essential for good health.
Bed warmers were displaced by hot water bottles, initially these were pottery bottles, the ones I remember were prone to leakage, these in turn were replaced by rubber ones which occasionally ruptured. However, the modern hot water bottle does not set the bed alight or leak unless strong drink has been taken before filling. The same ladies that had wielded the old bed warmers embraced electric blankets when they became available, this was a product that did not need a hard sell in the way that a waffle maker does.
The old bed warmers used heat that would otherwise have been lost whilst boiling a kettle to fill a hot water bottle increases energy consumption. I think the ladies would have seen this observation as a poor return for a university education.