Bursting in, be less coolheaded (8)
I believe the answer is:
sensible
'coolheaded' is the definition.
(thesaurus)
'bursting in be less' is the wordplay.
'bursting' indicates anagramming the letters.
'in'+'be'+'less'='inbeless'
'inbeless' is an anagram of 'SENSIBLE'.
(Other definitions for sensible that I've seen before include "Showing reason and sound judgment" , "Rational" , "Showing good judgment" , "Judicious line, Bess" , "Level-headed" .)