You don't want to leave the case completely open. A closed case provides an air path that directs airflow over the components. An open case won't have this airpath, and will actually provide reduced cooling in many cases. That's why, if you play with servers and removed the top or side cover while they're on, most modern servers will freak out and spin all the fans up to 100% and set a service code until you reinstall the top or side cover. While desktops don't typically have such a precision designed air path for cooling, it still applies. The air is taken in through the front and side, and drawn out through the top and back. This closed path doesn't allow air to stall and hang around certain components in the case.