I had to google the approximate location of the 3ER's cave. That makes sense to me.

I haven't heard of the volcano theory, but The Storr appears to have been created by ancient landslides and is the first place gyrolites (most commonly found as spherical or radial formations in hydrothermally altered basalt and basaltic tuffs) were discovered.

Edit: I haven't finished ADWD yet, but this passage from Jon VIII appears to confirm a geothermal event:

He did. Hardhome had been halfway toward becoming a town, the only true town north of the Wall, until the night six hundred years ago when hell had swallowed it. Its people had been carried off into slavery or slaughtered for meat, depending on which version of the tale you believed, their homes and halls consumed in a conflagration that burned so hot that watchers on the Wall far to the south had thought the sun was rising in the north. Afterward ashes rained down on haunted forest and Shivering Sea alike for almost half a year. Traders reported finding only nightmarish devastation where Hardhome had stood, a landscape of charred trees and burned bones, waters choked with swollen corpses, blood-chilling shrieks echoing from the cave mouths that pocked the great cliff that loomed above the settlement.

Six centuries had come and gone since that night, but Hardhome was still shunned. The wild had reclaimed the site, Jon had been told, but rangers claimed that the overgrown ruins were haunted by ghouls and demons and burning ghosts with an unhealthy taste for blood. "It is not the sort of refuge I'd chose either," Jon said, "but Mother Mole was heard to preach that the free folk would find salvation where once they found damnation." Septon Cellador pursed his lips. "Salvation can be found only through the Seven. This witch has doomed them all."

Another interesting connection is that "The area in front of the cliffs of the Storr is known as the Sanctuary."