I have to leave it open for now. I just got a used Celeron2@800 system (from Anandtech FS/FT) and it has a poor designed Inwin mid-tower. The PSU fan blows air on top of the CPU (whose fan blows air back at the PSU fan) and another fan blows in air from the front. No exhaust fans...so I leave the cover off.
With the cover on, I was getting idle CPU temps of 51C. I added a software CPU cooler and the idle CPU temp dropped to 42C. I removed the cover and the idle CPU temp is now 36C. Room temperature is 28C (stupid Alison is bring all this warmth to town), so I can deal with a 8C delta.