Moderately heated fight by militants in the beginning (4)
I believe the answer is:
warm
'moderately heated' is the definition.
'warm' can be an answer for 'heated' (I've seen this before). I'm not certain of the 'moderately' bit.
'fight by militants in the beginning' is the wordplay.
'fight' becomes 'war' (warring is a kind of fighting).
'by' means one lot of letters go next to another.
'militants in the beginning' becomes 'm' (I can't explain this - if you can you should give a lot more credence to this answer).
'war'+'m'='WARM'
Can you help me to learn more?
(Other definitions for warm that I've seen before include "(Of a scent) fresh" , "Cordial" , "Affectionate; quite hot" , "Approaching target" , "Affectionate; heat" .)