Heat loss through new chimney cowl, through new stove

Ok so my living room was south facing and if I shut the door it was the only room that gained heat through solar gain, however that has changed.

I had a 5kw inset stove placed in my chimney I had a 6inch flue inserted with a big cowl the anti bird ones.

The cowl at the top of the roof is much bigger than the old gas one and I get wind going down the chimney, I am convinced i am losing heat through this. Can I put a smaller cowl on? less than six inches? I am aware that you can get adaptors to change the flue but that would cost a forrtune, what can I do to stop heat loss

I am deeply disappointed with my stove I feel like I need to burn 5kilgrams of wood to maintain the tempreture I had previously with the chimney blocked off. Most of the heat seems to go through the flue. Any ideas?