Enclosed box...I am going to say yes. That is probably in the top 5 reasons why BMS units and inverters fail...enclosed spaces. If that BMS is maxed out at 200 amps, it is running at 5000 + watts! ?
I think that their cooling ability is dramatically reduced once they are in a small, enclosed area and the ambient temperature surrounding them continues to rise.
I would go through the extra trouble of attaching an additional heatsink if I were you. At minimum, a cooling fan at least the size of a PC cooling fan blowing right on the unit (80mm or so).
If your BMS and inverter are both in tight space, then I would have an opening with a fan evacuating air and be sure that the intake opening for fresh air is at least of equal size. I would say at least 92mm on the fan size.
Every time I watch a YouTube video regarding a failed inverter, it is nearly always tucked away in an enclosed space with no air evacuation = a coffin for the inverter. Then they wonder why the manufacturer will not honor a warranty claim.
In my Travel Trailer, the inverter, batteries and BMS are in the same environment as me - inverter on the wall, batteries and BMS in the open air of my cabin.
BTW: If you do not already have an IR temp gun, I would get one ASAP. Harbor Freight has one for $25. I consider this an essential device. You want to be able to instantly point at your inverter, batteries and BMS and know the real temperature. I depend on my trusty Fluke IR gun and I would never be without it. You also want to be able to point at battery conductors and the AC input/output wiring (especially at the terminal) and see temps.
I melted the neutral input terminal of my 3000 watt inverter and had to replace it. The cause? Severe arcing at the 30 amp connector plugged into the pedestal. I hit the neutral side of the 30 amp plug with my temp gun and it was 200 F!!! That is crazy arcing and it will cause higher current draw for that conductor, along with rising heat. Plugs, sockets and terminal connection are so very critical and I think most people don't think about them much.