Probably not, they're not usually insulated underneath, to my aging experience. So putting a lid on it wouldn't keep the other surfaces from leaching away heat
It doesn't have to completely prevent heat loss, just long enough for a good part of the day, and of course you'll refresh the hot water daily haha.
Right, but I don't think it'll buy more than a half hour, it'll lose that much through the tub itself. Experiment if you can justify it! I'm wrong a lot. I suspect that you'll be disappointed with the results, though.
I don't think most bathtubs are insulated on the sides/bottom. At least not older styles.
Any heat that you trapped at the top would escape out the sides/bottom after a lot shorter amount of time than even 8 hours.
What you're looking for is a eastern European/siberian banya style tub setup... And no that's not just a lid. You need lots of insulation and insulting interfaces between spouts and pipes. Even then those only stay hot for like 3-4 hours.
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