Can't answer for aluminium, but I can answer for window glass: One of our plants was threatened by massive flooding 2021, threatening the float glass oven (which doesn't float itself despite the name). It was closed off with insulation, turned off, and everyone hoped for the best and no steam explosion. In the end, only the cellars with the control equipment flooded and it could be gradually (as the control cabinets were checked and restarted) brought up again without loosing too much heat a day later.
In short: Heat Inertia of large molten bodies is massive with good insulation. If the time is too long tho, only dynamite will dismantle a solid chunk of material again.
Its not an oven alone, its a kiln that smelts up the components for glass of the desired recipe, then purs the glass on a long (~half a km) basin of molten tin where it stretches and cools slowly, pushing the solidifying mass down the basin until the end. Re-Melting it is as far as i know not possible, as the melting is done before the pouring. You can melt the tin again, but not the glass.
Interesting! Does this mean that you could use intermittent energy sources, like solar power, to heat up the float glass oven during the day and it woul keep enough heat during the night so that it could keep running in the morning?
Float glass is a continuous process, so it runs 24/7 and too much product is recycled into the smelter at the start again (Funnily, glass waste is actually a scarce resource). Getting the process dialed in to emit the desired quality is a long winded thing as far as i know (not involved in the process myself). Also, the heating is done with gas (LNG/CNG/H2) and electric in combination.
The Insulation is in place all the time because the process is very energy intensive and the glass over the whole basin is supposed to cool evenly. Just the end is not closed off as the glass is ejected in a continuous endless stream[1].
In short: Heat Inertia of large molten bodies is massive with good insulation. If the time is too long tho, only dynamite will dismantle a solid chunk of material again.