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Especially if the bathroom door was closed, it doesn't surprise me. Water holds heat about 1,000 times more than air does. (Called thermal mass.) If the water started at 106, it could take a while for it to cool to 93. If I don't drain the tub at night, it's still noticeably warm in the morning.
You may have noticed your car engine stays warm for several hours. Heavy things cool slowly and a tub of water is about 700 pounds.
With the door closed, once the heat from the tub warmed the air in the room, the heat would escape even more slowly through the walls.
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