The Pentium chip runs much hotter that earlier CPUs. The Pentium chip operates at about 185 degrees Fahrenheit. The Pentium 133 above needs the airflow across the chip to cool it. A heat sink moves the heat away from the chip and into position for the fan to blow the hot air away. Notice the metal fins that wick the heat away.
Thermal grease improves the heat conductivity between the processor and the heat sink.
Most thermal grease is silicone based. If you run into the old thermal grease which was mercury based, be sure to avoid contact with your skin. Running a Pentium chip with no fan, even for a short time, can destroy the chip and the motherboard.