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First and foremost is Adamantine. No normal substance can harm adamantine, cause it to lose shape or edge, and among "abnormal" substances the only one known to even pose a threat to adamantine is icemold (see below). Adamantine appears as either a tan stony substance or a steely metallic substance, although different ancient weapons-mages and craftsmen often "signed" their creations with special tinges or colors. Adamantine items are relics from a time before and during the Wars of the Tap, and can only be made by a mage using the entire Eternal Tap. As such, no adamantine items have been made since the end of those wars. Based on ancient texts, the only known method of creating adamantine suggests that it is an alloy, as it describes a process by which mythril and prevalida ores are melted together over a fire stoked by liviol wood and kindled on a bed of Njalian Spidersilk; the entire thing must, of course, be presided over by a mage feeding the power of the Eternal Tap into the mixture. There may still be other means, altogether unknown, of crafting adamantine, but anyone who discovers such a method is bound to keep it a dead secret in order to maintain the high price of what they create.
There is no description mentioning any capacity to eat magic, and none of the players currently using adamantine weapons seem to be aware of this new property you speak of (infusing Tap Magic during the smelting process implies no inherent ability to absorb any and all magic, the same way an enchanted weapon does not). While it does state indestructibility, it does not say anywhere that the metal does not vibrate: in fact, the simple fact that knocking on adamantine would create a sound means that it would be able to vibrate, and thus, to absorb heat (as heat would increase the vibration of its particles). As long as the adamantine did not melt or lose shape (which it did not), then heating up the area either through physical or magical means would be physically viable, and does not violate any of the specified properties of adamantine in the canon accessible to players.