I found that PC cases with the case ON are cooler than with the case off
With a good airflow design yes, but my current machine overheats within 10 minutes of having the case on - it's fairly black and white. The problem is my second hard disk which is overheating and unfortunately it's located too close to the air intake fan.
It's a heavy & noisy 15 year old server full tower case, and it's going to be scrapped... ! :)