At heart, Caligula's terribly cross (4)
I believe the answer is:
ugli
'cross' is the definition.
(I've seen this before)
'at heart caligula's terribly' is the wordplay.
'at heart' indicates the central letters.
'terribly' indicates an anagram.
The middle of 'caligula' is 'ligu'.
'ligu' is an anagram of 'UGLI'.
(Other definitions for ugli that I've seen before include "Black/violet element" , "Citrus fruit cross (which sounds offensive!)" , "West Indian citrus fruit" , "Grapefruit/tangerine hybrid" , "(Repulsive-looking?) fruit" .)