After testing for a while, I noticed cooling jacket doesn't work in marksmanship mode for the N-Tec 7c 'New Glory'. It works fine when hipfired though.
I see no reason for it to not work while in marksmanship mode, so I am assuming it is a bug.
I also did a quick google and someone already did a video shooting the gun side-to-side with and without cooling jacket 3: