Cold girl getting degree, the heartless student you study with (9)
I believe the answer is:
classmate
'student you study with' is the definition.
'cold girl getting degree the heartless' is the wordplay.
'cold girl getting' becomes 'class' (I can't explain this - if you can you should give a lot more credence to this answer).
'degree' becomes 'ma' (Master of Arts is a type of degree).
'heartless' says to hollow out the word (remove centre letters).
'the' with its middle removed is 'te'.
'class'+'ma'+'te'='CLASSMATE'
(Other definitions for classmate that I've seen before include "someone from school?" , "one of the others being in form" , "Fellow student" , "Schoolfellow" , "Fellow pupil" .)