Your cabinet fan would have work better if it has only limited opening at the back of the cabinet. Instead of a single huge wire mesh, one solid ply and hole for the fan only. So fresh air suck from cabinet slits outside, pass through the only way out which is the by the fan blower. And you have to have a slightly wider gap from the wall as the hot air will just get back in if it's too close unless it's one solid piece backing.