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>This means that the temperature at the bottom of the pond will rise to over 90 °C while the temperature at the top of the pond is usually around 30 °C.

Can that really be right, it seems like a very high gradient.

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Depends upon the depth (and geometry) of the pond. Without convection, some of our intuition for thermal conductivity in liquids and gases is lost.

I'm not sold on the numbers, but I'm also not yet convinced of the idea's physical impossibility.

Water has quite low thermal conductivity (~0.6 W/(m*K)). If you exclude convection you can easily have such a temperature difference. For example with heat flux of 100 W/m2 you have 60 K temperature difference over a 36 cm thick layer of water.

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