Exactly the opposite is true. Metal has a much higher specific heat capacity than plastic. It is also much more thermally conductive. So when you put hot water in a metal bath its heat is not only very quickly shared between the water and the bath (resulting in a lower average temperature), but it is conducted to the outside surface of the bath where it is radiated away. The metal is warmer to the touch, which may give the illusion that it is "retaining the heat", but in actuality the reverse is the case.
Exactly the opposite is true. Metal has a much higher specific heat capacity than plastic. It is also much more thermally conductive. So when you put hot water in a metal bath its heat is not only very quickly shared between the water and the bath (resulting in a lower average temperature), but it is conducted to the outside surface of the bath where it is radiated away. The metal is warmer to the touch, which may give the illusion that it is "retaining the heat", but in actuality the reverse is the case.
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