I hadn't been thinking about battery life for the Wu screen. Man, I hope you won't be spending a lot of time using the charge and play cable ...
I'll take a guess at about half of that!
The way the GC and Wii are designed you get air effectively ducted over the heatsink, which is the same thing as having a fan on the heatsink (barring any push/pull differences). In something like the Wii, adding a fan directly to the heatsink would mean a shorter heatsink, interrupt air flow through the case and may actually reduce overall cooling effectiveness. Unlike PCs the cooling has to be considered for the system as a whole rather than on a per-component basis. Even "passive" GPUs in the PC space require good "active" case cooling for anything other than the most scrubby of GPUs!
Thermal issues place a cap on performance even in the PC space (look at CPU TDP ratings for example) and that's despite decades of experience, the most advanced fabbing processes on earth (Intel are giants) and the capacity for much larger and much more expensive cooling solutions. There's no getting away from the heat issue unfortunately!