Well excuse me for being pedantic but it does say "simply because seawater would continue warming up, which makes it expand", So any of your ideas about all the rest of it are neither here nor there if we are to take this statement literally. Plus it has everything to do with water in test tubes. It's all H2O and it all expands at the same rate.
Did you know by the way that the amount of evaporation is exponentially proportional to temperature? How much effect this will have is something I have not calculated but it's worth considering. Plus of course you know it will form clouds and the clouds will block out the sunlight. So 'simply' was the wrong word to use.
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