Some comments:
A. All of the equipment within the box may be designed and rated to run at the temperatures that concern you. They also may not be. You could measure the temp (properly closed) the inspect the major components to see if the operating temp is within the design of the components. The wire might be included.
B. While everything with current flowing thru it gives up some heat, you might find the significant contributor by examination or measurement - measurement with IR or similar meter. Replacement of an item, the wire, whatever, might keep things a little cooler.
C. As already suggested, the cabinet is there for a reason and is likely a code requirement. Operating with the door open increases risks of injury or failure (dirt, dust, metal chips, etc). It probably should be closed.
D. A fan with a filter could be provided which helps ease the contamination concern however it may create a non-compliance issue in that the cabinet or enclosure may no longer meet the requirements for the application.
I (and I know others feel the same way) feel like I over-emphasize compliance with rules or I get picky with modifications but in many situations it is of critical importance. I've spent the last zillion years inside industry and it does matter.