Typical servers are 1U or 2U high boxes. 1U=44.5 mm and each box is "full depth", so around 700 mm long (sometimes more), and ~450 mm wide. The 1U boxes typically just have a block of copper with a dense bunch of fins on them as a CPU cooler, while 2U designs usually incorporate heatpipes.

Lots of airflow.

High-density systems are usually 2U, but with four dual-socket systems per chassis.