AMD BOX Car Freezer cooling?

I just started a project of building a custom full aluminum case/cooling for my PC.

It will have the shape of the AMD logo, so i will get all the components (except for the CD-R) at 45º. But this has nothing to do with the cooling part...

So the thing is I saw a 50 bucks car drink cooler working out of the 12V cigarette output of the car, so i thought i could dissemble it and use it to cool my system, but i don't know if it would be better to connect the gas system directly to the CPU/GPU(2X) blocks and insulate all the loop or to chill the water first, and use a standard water cooling system.

Any suggestions?

I highly doubt it will have near enough cooling capacity to cool the loops down at all.

Just try and fit a decent rad into the case.

won't do much if anything.

The load of your CPU and GPU will eventually overcome the cooler. What would happen, is that it would slow the heating of the water until it overcomes the unit's thermal limit. The cooling element, which is likely thermoelectric, will not offer enough cooling to keep the constant load at bay. It will eventually burn out.

And by eventually, I mean this will probably happen in the course of a few minutes. :-\