I have a tiny, six-pack-sized cooler that fits nicely on the front rack of my little bike. I've occasionally thought it would be handy to have a larger cooler that fit, pannier-style, on the rear rack of my larger bike, but I worry that a DIY job might compromise the insulation of the cooler and leave some of the attachment parts socking in ice water, which might not be good for them.

But I did find a solution to wanting a bigger cooler by turning again to the little bike with a wide rear rack.
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I've also heard of people using water-proof panniers to as temporary coolers by throwing ice in them along with their cold items. Of course the panniers aren't insulated, so that wouldn't be good for very long, and they're soft-sided, so it wouldn't be good with items that could be crushed.