That man’s method of kindness... (5)
I believe the answer is:
heart
'kindness' is the definition.
(thesaurus)
'that man's method' is the wordplay.
'that man' becomes 'he' ().
'method' becomes 'art'.
'he'+'art'='HEART'
'of' is the link.
(Other definitions for heart that I've seen before include "Centre; valour" , "bottle" , "Blood-pumping organ" , "Vital organ - centre - courage" , "Middle" .)