I've just done a bit of research and apparently the point of cooling it (as partly explained by you above) is to let the grains of rice separate from each other and the whole mixture isn't so glutinous and flavours react differently to it.
The best way I can think of doing is by laying the hot rice on a lined baking tray that's been put in the freezer, then put it (with the rice on) in the freezer for just 5 minutes say as not to freeze the rice and ruin the texture. This seems the most logical way as it means the rice has the largest surface area to cool down.
Another way if the first is not possible (although not as good) is by putting the hot rice in a thin metal bowl above some ice water but of course you cant stir it or the gluten will come out and you'll end up with a sticky ricey mess!
Hope this helps!