You're in a tough place there. A fan in an enclosed cabinet won't do you any good, you need a fan drawing cooler outside air somewhere, as well as an "exhaust" for warmer air to leave. With that cabinet sat against the fireplace to the side and a wall behind it, I don't think you can accomplish that.
I have my PC tower inside of a cabinet. On the side of the cabinet I have 2 PC fans pulling cooler air in and on the back I have 2 fans exhausting warmer air out. This picture isn't my setup, but it looks similar.
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