Technically not by convection because that is the movement of fluid to transfer heat in and out of something, like air conditioning. The bath is not a moving fluid it is a simple constant temperature. The spinning moves the fluid inside the can so more of it touches the aluminum wall, which is being cooled by conduction with the ice bath.
There are dozens of choices that work great for twenty some dollars online here in the US and don’t even replace the seat.
You can definitely get one in Australia. They are like $30 on the internet delivered right to your house and attach to your toilet in under 5 min.
All normal modern ones are just a simple toilet add on. Take up no space whatsoever.
There is a long and very simple history here. Japan had an entirely different assembly process from the US when they started making cars and simply were at first universally more reliable than all American cars, by huge margins too, for many decades. This is not as true as it used to be but still holds in some cases and has been true for so long that it is accepted as true.
So in a conversation about someone commiting a hate crime based on someones genetalia you decide to use a term specifically used to debase people by calling them female genetalia and it seems people even upvote you for it. Great. And you even think you are being supportive.