I'm surprised there isn't a surround that stops the heat from just passing through the coils, and a stove pipe with damper to control the heat of the fire. I have a snorkel stove in my hot tub with a stove pipe and damper. It still gets too hot, but is easy to cool down by adding fresh cold water.
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This is a cross section from when I replace a rotten end. Stove is 40 years old, the tub is about 15 year old and has had both ends replaced.
Carl.