How do I get Rhot's heart?
I don't know the prerequisites, but you get it by sleeping there at the temple in the chambers Othra prepared for you.
It takes several instances. You'll get the feeling that someone was watching you sleep if you've met all the requirements. Over time you keep an eye out for who is intruding on your space, and if you make the right choices, you can invite him to spend the night keeping warm with you. That gives the heart.