The most common and most likely answer to this crossword clue is the 13 letter word SUPRATEMPORAL
S
U
P
R
A
T
E
M
P
O
R
A
L
Buddy explains!
The straight part
We know that "off the top of one’s head?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case off the top of one’s head? = supratemporal.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.