You don't want the heatsink to retain heat.  You want it to exhange it with the environment.  In this case, the only option is natural convection with air.  We don't ever want the chipset to overheat, so we design from steady-state at the maximum allowable temperature.

R = (T_max-T_out)/Q

Where R is the thermal resistance of the system, Tmax is the maximum allowable temperature of the chip package, Tout is the highest expected ambient temperature, and Q is the heat output of the system.  R is your only unknown, and is your design variable.  Using the above equation, the maximum allowable thermal resistance can be determined, and then the system can be design to be below that resistance.

Thermal resistance, R, is going to be the sum of several different things, but as it relates to the heat sink, it is a function of fin effeciency (which is a function of geometry), surface area, and heat transfer coefficent (which is a function of fluid flow and characteristics).  Mass is not a design variable to be considered, even in a redesign.  Space requirement do need to be considered in this redisign since those have already been set.

You mentioned increasing the mass increases the effiecency of the fins, but increasing the thickness of the base (which is what I think you meant) will actually increase the overall thermal resistance of the heat exchanger.

Now that I'm thinking more about this, I wounder how this is going to work since bouyancy and gravity become important for natural convection.  It would still need to work for both the upright and flat Wii configurations.

Edit:  Besides the fact that mass does not appear in any of the relavent equations for heatsinks, there is another way to look at this.  If mass was important, then denser materials would be used, since they have more mass per unit volume.

Wii doesn't have the horsepower to emulate GC. That's not even a consideration at Nintendo. It's also a waste of resources since it operates internally as a GC on its own rendering emulation a poor option to begin with.

So it is entirely impossible to have GC game saves on a SD card and play the games with a classic controller? ENTIRELY IMPOSSIBLE?

Impossible...probably not but improbable.  The GC portion of the Wii has no drivers for the non-GC controllers or access to the external memory.

Nintendo has not altered the GC portion of the Wii in any fashion from the actual physical GC unit so don't expect them to alter anything in the future.

Restart yourself, throw some chairs, scream and dance, it should work. If not, try uninstalling unnecessary organs or limbs.

Nice move by Nintendo.

@theRepublic: I wasn't only meaning thickness, but that's pretty much the only way to add mass without changing the qualities of the alloy itself.

You need to have a certain heat resistance in order for the heat to store into the matter to transfer it elsewhere in the matter, that's why the base of the heatsink is so thick instead of being foil that would have a lot smaller heat resistance. Bigger mass makes it possible to transfer bigger amounts of energy. Of course, the bigger heat reserve of bigger mass makes it less efficient for the heat to transfer from the processor to heatsink.
I'm starting to have a feeling that we aren't disagreeing, we just look at the same thing from different perspective.

In mass production all the design work starts from the cost efficiency standpoint (of course, it wouldn't make much sense to design something useless just because it's cheaper). The more mass you are going to use, the more expensive your product will be, but the matter you use must be suitable for the purpose. It wouldn't make sense to make an heat exchanger out of plastic because it's cheaper and on the other side of things, making the heat exchanger out of diamonds doesn't make sense because of the high cost.
If you can save ten cents on a product that is sold a million copies, you've saved a designers 1-1,5 years expenses.

Btw. How much more efficient, than the current, the heatsink should be by your judgement?

@Lightbleeder: I don't see that it would be impossible for Nintendo implement. Basically all that would need to be emulated would be controller and memory card. But as long as the controller ports and memory card slots are there, there's not that much sense in emulating.