It depends on the design of the case, including fans and interior
layout...
Old airplane engines were air-cooled by airflow over the cylinders
that simply stuck out in the breeze. Later, cowls were put over
them to reduce air drag. Some intelligent people discovered that
a cowled engine also stayed cooler, and that evolved into today's
closely cowled engines in almost all piston engine designs.
However, those designs must be deliberately designed to ensure
cooling air to all the cylinders.
Likewise, an open case will likely adequately cool a low-power
system. However, in a higher power system, airflow through the
case has to be engineered to cool the motherboard chips
("Northbridge" and "Southbridge"), graphics processor (GPU), and
hard drives as well as the CPU. If you look in a higher power
system these days, you will find large finned heat sinks on all
these components. Good airflow over all these components is
crucial, and may be enhanced by a closed case with well-placed
fans.