Most of the heat is conducted out through the lead frame. Typically the drain connection has the most direct connection (thermally) with the lead frame, so having multiple pins to conduct the heat out to the PCB is optimal.
Sometimes the gate and source are connected to the other pins with bonding wires (perhaps many in parallel in the case of the source, to reduce resistance), sometimes with a second clip part that goes overtop of the die, but in both cases the drain is a more direct thermal connection to the die.
Bonding wire design from here:
Newer clip style from here:
Having as much copper as possible connected to the drain pins will help dissipate power, as will having power planes as continuous as possible under the part.
Many more modern packages have better thermal performance than the SO-8, when properly mounted.