Lack of warmth sees English Christian back in coat (8)
I believe the answer is:
froideur
'lack of warmth' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.
'english christian back in coat' is the wordplay.
I cannot really understand how this works, but
'english' could be 'e' (abbreviation) and 'e' is found in the answer.
'back' could be 'fro' ('fro' can be a synonym of 'back') and 'fro' is located in the answer.
This explanation may well be incorrect...
'sees' is the link.
(Another definition for froideur that I've seen is " Reserve (between people)".)