As a whim a fatheaded advert (3)
I believe the answer is:
fad
'as a whim a' is the definition.
I can't tell whether this definition defines the answer.
'fatheaded advert' is the wordplay.
'fatheaded' becomes 'f' (this could be a standard abbreviation I've not previously seen).
'advert' becomes 'ad' ('ad' can be a synonym of 'advert').
'f'+'ad'='FAD'
Can you help me to learn more?
(Other definitions for fad that I've seen before include "A passing fashion or craze" , "Passing craze or peculiar notion" , "A craze or current vogue" , "Passing vogue or fashion" , "Passionate interest" .)