For us carb mount filter guys, I haven't tried this yet but what if you take your unused airbox and slip in a metal or plastic liner, then use sprayfoam to fill the gap around the liner for insulation. Some foam glued to the lid and you have a little cooler. If you drilled it you could even use the drain.

 

I put some duck tape on mine, and I could fit 5 bottles of water and a few chunks of ice. It works pretty good. Only problem is the pipe is close to the box and melts the ice. But your idea might work better.

Bat

 

I tried sticking water botttles in mine but the box picks up alot of heat from the pipe and engine. That's where the insulation comes in.