No, I don't think so.
I will burn the heart out of you.
Assuming that the speaker isn't standing in front of the listener with a red hot poker or a laser gun, the above sentence clearly indicates that the speaker is trying to destroy the will out of the listener.
I will burn your heart out.
"Your heart" at first seems to indicate your biological heart, but when you analyze the whole sentence you can ascertain that "your heart" means will. This structure isn't grammatically wrong, it just isn't as fluid to me as the first sentence.
I will burn the heart of yours.
This seems really clunky. Again it isn't grammatically wrong, it is just an odd phrasing that is rarely used. I'd always say "my car" and never "the car of mine."