Pretty sure there is no hot water feeding the toilet. If the water was hot, it makes me think something was heating it. Like maybe the sensor that shows how full it is. Maybe it shorted out and heated the water. Perhaps some other electronics under the bathroom area was shorting and heated the water.
Toilet feeds your black water tank. The water overflowing your toilet was black water. If your grey is leaking, that issue maybe related to what ever heated your water, but it should not be caused by an overflow of your black tank / toilet. Sounds like something cracked or melted a hole in your grey line after the valve, otherwise it would leak all the time.
I might be way off here, but hot water in a black tank doesn't happen from a toilet.
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