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If there were any rubber hot water bottles while I was growing up in the 1940s, I never saw any.
We had one hot water bottle in the house, and it was stoneware which is a certain clay fired at a particularly high temperature and glazed so that it resembles polished stone. In fact stoneware was often just called 'stone'.
Our stone hot water bottle was only used on very rare occasions. Probably my mother was scared. with some justification, that it would crack or leak, which would burn someone and make the bed wet. However, she never gave those reasons. It was always - so she said - that it was healthy to get into a cold bed and warm it up oneself. As a child I believed her, although in winter it was very cold in bed, as no fire was ever lit in the bedrooms and the windows were single glazed. It was not uncommon to wake up to ice on the insides of the windows from frozen condensation.
These stoneware hot water bottles had been around since the early 1900s and possibly before. The idea was to fill them with hot water, close the stopper securely and stand them in a bed, upright, on their small flat ends so that the sheets and blankets formed a tent-like structure over them. The peak of the 'tent' was the special feature of the rounded knob opposite the flat end, which also served as a carrying handle.
Used this way, the hot water bottle was supposed to heat more of the bed - but it was an unstable arrangement and the 'tent' would have been quite small, as even with the knob to give extra height, the hot water bottle was not very tall. I suspect that most people used the bottle in the position shown in the photograph.