Witchfire Standing Torches reduce heat by 5 in a tiny area around them. In theory you could crowd a ton of them around your logout spot and hope that that, plus your Silent Legion armor, would be enough.
But there’s one more crazy thing you could try: it turns out that plain old Sandstone building blocks reduce heat by up to 20 if you’re in a small room. (I’m not 100% sure how this works. I think that it’s -5 per building block that you’re standing close to, so if you’re in a corner of a single-story room that’s two walls plus the foundation block plus the ceiling block.) That plus Witchfire torches plus Silent Legion armor should, if I’ve done the math right, make it safe to log out in the volcano.