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There's actually an even more common example that what you've described: water heaters. The cold inlet at the bottom and the hot outlet at the top prevent mixing, and the two waters of different temperatures can maintain their difference for a surprisingly long time.

https://www.youtube.com/watch?v=Bm7L-2J52GU

(technology connections describing it)

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I guess what we often ascribe to diffusion (hot and cold water mixing in a glass) is helped along tremendously by convection. But convection might get more easily started in a glass if the center and the sides are different temperature. Then you get this loop. But it might then not happen in a water heater since there's no lateral temperature differences.

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