Yes Brian, that's exactly what came to my mind. The bike is heavy enough without an extra two or three gallons of water (a third again heavier than gasoline, per gallon) sloshing around in the top box.
I mentioned a Peltier Junction solution a short while back. It turns out there are devices (sub-assemblies, actually) that might work with only sufficient fluid in the system to achieve circulation - maybe a pint or two. My research suggests that a total package, including reservoir, pump, heat exchanger, and piping into a vest might weigh between seven and ten pounds - not trival, but not excessive either. The price might be an issue: I can't see the components along costing any less than about $300.
I will look into the idea, though. If the concept of a jacket with flexible tubing has already been hoisted up the flagpole and folks have not laughed it off stage, then I assume people would at least be willing to give it a look.