It would cut down foaming, but it won't help with heat exchange. Heat transfer is always dependent on the surface area. One big bubble has less surface area than N smaller bubbles of the same total volume. (As you take a big bubble and make N smaller ones, the total surface area available for heat transfer increases as a function of the cube root of N.)
Also, air isn't a good conductor of heat -- it has a high R value -- which is why it works in double-pane windows. When I measured the difference with bubbles and without, I got _maybe_ 0.1C, less than the measurement error of the thermometer.
That's a clever idea -- lots of surface area, copper is a great heat conductor, and it's a cheap source too. To make it most effective you'll have to make sure the copper is exposed to room temperature or colder.





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