Hi,
You really need both. Aluminium is used to absorb heat from the chip, ususally with a thermal transfer paste between the two, just to help connect the two thermal bodies. The heat sink transfers energy into the surrounding environment via both radiation and conduction.
If there is no forced movement in the surrounding air (or water, etc), then before too long the air gets warm. Quasi equilibrium is reached when there is a stable thermal gradiant in the air surrounding the heat sink. Heat is then primarily transfered via diffusion/convection through the air, as well as the afore mentioned radiation. Note, that although the system is in a reasonably stable thermal state, it is an open system, and there is still net heat transfer through the air. Obviously, if the air is only being moved by the thermally generated diffusion/convection processes, it trasnfers much less heat than if cool air is forced over the heat sink. If you move air with a fan, the heat is dispersed throughout your study room, instead of being so localised around your chip.
Heat sinks are designed to have good thermal conductivity, large surface areas, and often surface treated to improve radiation in the peak bandwidth for the expected temperatures.
Without either the heat sink or the forced air flow, there is much less heat transfer away from the chip.
Hope that helps.