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One could hypothesize that the walls of the extradimensional space have a constant temperature X, that is inferior to lava's temperature, which results in a constant heat flow from the lava to the wall of the space. If the extradimensional space is a perfectly closed system, like a perfect thermos, then yes one could keep ice or lava in there.
Trying to apply real physics to magical effects is always fraught with peril. The interior of a Portable Hole is an extradimensional space with finite boundaries, but those boundaries aren't really "walls" in any conventional sense; they're planar boundaries. I'd say that heat can't dissipate out through those boundaries when the opening to the hole is closed for the same reason that PCs can't tunnel their way through them: there's simply nothing beyond them; nowhere for the heat to escape to.
I would argue against it for the very reason outlined here, as the item was probably not designed to be weaponized as such.
If you're looking for a way to limit what PCs can place within a hole, I'd propose looking at the nature of the item itself. A portable hole is essentially a circle of magical cloth 6-ft across. Even when placed upon a flat surface and the center of the cloth effectively disappears, some measure of it's cloth edges remain; characters need that edge so they can pull the hole away from a surface. Having that fabric edge where lava (or acid) can flow over it into the hole would seem to be a very bad idea. If the fabric suffers sufficient damage, the item will eventually be destroyed. Certainly there are workarounds that clever PCs can devise to get damaging substances in and out of the hole safely, but it's still a risky proposition; one which thrifty PCs may prefer to avoid for fear of loosing an expensive item. Just my 2¢.