The bones of broadcasting unit briefly close to his heart (5)
I believe the answer is:
radii
'the bones' is the definition.
(radius is a kind of bone)
'unit briefly close to his heart' is the wordplay.
'unit' becomes 'R' (R is an example).
'briefly close' becomes 'adi' (I can't explain this - if you can you should believe this answer much more).
'heart' means to look at the middle letters.
The centre of 'his' is 'i'.
'r'+'adi'+'i'='RADII'
'of broadcasting' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for radii that I've seen before include "spoke with others" , "Veins of insect's wings" , "spoke several times" , "Straight lines from the centre to the surface of a sphere" , "Spokes of wheel - bones of arm" .)