I know that the Karmapa used it to describe his FOUR HEART SONS.
Does anyone know the history of the term HEART SON?
I don't know the history of the term but it is sure to stem from a specific Tibetan word or phrase and does indicate an intended future lineage holder when used in TB religious politics although as noted by a previous poster it's really just a term talking about an extremely close student (student or disciple is not quite right) - Marpa and Milarepa are the classic examples - karmically connected guru and disciple bonded like family.
The concept is also found in China and may or may not stem from Chinese culture (or it may stem from West Asia culture going way back). The best examples are from martial arts where a close student can be seen as a kind of adopted son/daughter of the master.
_________________Kirt's Tibetan Translation Notes
"Only you can make your mind beautiful."
HH Chetsang Rinpoche