Cool one's ardour in court (13)
I believe the answer is:
dispassionate
'cool' is the definition.
(thesaurus)
'one's ardour in court' is the wordplay.
'one's' becomes 'i's' (Roman numeral).
'ardour' becomes 'passion' (I've seen this before).
'in' indicates putting letters inside.
'court' becomes 'date' (romantically pursue).
'is'+'passion'='ispassion'
'ispassion' put into 'date' is 'DISPASSIONATE'.
(Other definitions for dispassionate that I've seen before include "Imperturbable" , "Rational, impartial" , "Objective, unemotional" , "Not affected by personal feelings" , "taking the unbiased view?" .)