Good read, Nobody! Found myself nodding many times (6 and 7 especially), and have used a similar approach over the years. The only way I would be pissed off with this, is if i happened to be playing a redundant PC cleric/priest of a Luck god/goddess :P Go to Comment
The tree isn't really magical, it just uses principals that we don't see on earth. It uses the heat from the magma as a source of energy. It would probably have warmth, but essentially, the tree is converting the heat into stored energy, eliminating most of the heat itself, which, solidifies the magma into rock.
So, it would radiate heat, but much less than you might expect. Go to Comment
1) It could bleed off heat in any process the GM wants. Water is an easy, and thematically appropriate way to handle, but certainly not the only way. I have made no provisions for other ways to bleed off heat.
2) I will add in my post that it could be held, but you would want to wear gloves. It's kind of like real life dry ice in that respect. The heating, and cooling is gradual enough that it shouldn't be usable as a weapon.
3) It can absolutely be shaped, worked into other materials, used for decorations. It's a mineral. The whole point of simple materials like this, is to blur the annoying line between magic and mundane, in an almost believable way. Go to Comment
I like magical materials, but something seems off using them to create hot springs.
So access to the correct substances essentially disables its physics-bending features, turning it into simply really hot stone. This heat would transfer to the local liquid, heating it. This would continue until the stone was out of latent heat and matched the water's temperature. Unless the water was subsequently removed, it would not gain any additional heat and everything would return to normal until the water left in some manner.
Now, if the algae were killed when the water got too hot, and began to grow when it cooled off again, then I could see a sustained cycle occurring, keeping the water at the desired temperature for the algae.