Okay, now he knows who this is. The TARDIS had told him that she had once been trapped in a human body, that it had died around her. This must be that body. The bit about dead TARDISes he doesn't entirely understand, but it's not exactly the most comforting thought, either.

What is clear is that this body can't contain everything that should be running through the TARDISes mind. He reaches out both of his hands to her and sets them on her upper arms, hoping to pull in her focus. "I know a future version of you. I know you, yeah? You make it out of this. The situation and the bod." Belatedly, he remembers that she likes mental comfort, so he tentatively reaches out to her mind as well, giving it the same care he might with a human.