Scottish engineer ignoring cold woman (5)
I believe the answer is:
madam
'woman' is the definition.
(used to address a woman)
'scottish engineer ignoring cold' is the wordplay.
'scottish engineer' becomes 'McAdam' (18th- and 19th-century engineer John Loudon McAdam).
'ignoring' suggests deleting specific letters.
'cold' becomes 'C' (eg on taps).
'mcadam' with 'c' taken away is 'MADAM'.
(Other definitions for madam that I've seen before include "precocious schoolgirl?" , "How one may address a woman" , "Woman with status - girl with bad manners" , "Titled lady" , "Formal address to a woman - precocious little girl" .)